All papers in 2022 (1246 results)

Last updated:  2022-09-19
Identity-Based Matchmaking Encryption from Standard Assumptions
Jie Chen, Yu Li, Jinming Wen, and Jian Weng
In this work, we propose the first identity-based matchmaking encryption (IB-ME) scheme under the standard assumptions in the standard model. This scheme is proven to be secure under the symmetric external Diffie-Hellman (SXDH) assumption in prime order bilinear pairing groups. In our IB-ME scheme, all parameters have constant number of group elements and are simpler than those of previous constructions. Previous works are either in the random oracle model or based on the q-type assumptions, while ours is built directly in the standard model and based on static assumptions, and does not rely on other crypto tools. More concretely, our IB-ME is constructed from a variant of two-level anonymous IBE. We observed that this two-level IBE with anonymity and unforgeability satisfies the same functionality of IB-ME, and its security properties cleverly meet the two requirements of IB-ME (Privacy and Authenticity). The privacy property of IB-ME relies on the anonymity of this two-level IBE, while the authenticity property is corresponding to the unforgeability in the 2nd level. This variant of two-level IBE is built from dual pairing vector spaces, and both security reductions rely on dual system encryption.
Last updated:  2022-09-19
On Generalizations of the Lai-Massey Scheme: the Birth of Amaryllises
Lorenzo Grassi
In this paper, we re-investigate the Lai-Massey scheme, originally proposed in the cipher IDEA. Due to the similarity with the Feistel schemes, and due to the existence of invariant subspace attacks as originally pointed out by Vaudenay at FSE 1999, the Lai-Massey scheme has received only little attention by the community. As first contribution, we propose new generalizations of such scheme that are not (affine) equivalent to any generalized Feistel scheme proposed in the literature so far. Then, inspired by the recent Horst construction, we propose the Amaryllises construction as a generalization of the Lai-Massey scheme, in which the linear combination in the Lai-Massey scheme is replaced by a non-linear one. Besides proposing concrete examples of the Amaryllises construction, we discuss its (possible) advantages and disadvantages with respect to other existing schemes/constructions published in the literature, with particular attention on the Lai-Massey one and on the Horst one.
Last updated:  2022-09-19
A Modular Approach to the Security Analysis of Two-Permutation Constructions
Yu Long Chen
Constructions based on two public permutation calls are very common in today’s cryptographic community. However, each time a new construction is introduced, a dedicated proof must be carried out to study the security of the construction. In this work, we propose a new tool to analyze the security of these constructions in a modular way. This tool is built on the idea of the classical mirror theory for block cipher based constructions, such that it can be used for security proofs in the ideal permutation model. We present different variants of this public permutation mirror theory such that it is suitable for different security notions. We also present a framework to use the new techniques, which provides the bad events that need to be excluded in order to apply the public permutation mirror theory. Furthermore, we showcase the new technique on three examples: the Tweakable Even-Mansour cipher by Cogliati et al. (CRYPTO ’15), the two permutation variant of the pEDM PRF by Dutta et al. (ToSC ’21(2)), and the two permutation variant of the nEHtM\(_p\) MAC algorithm by Dutta and Nandi (AFRICACRYPT ’20). With this new tool we prove the multi-user security of these constructions in a considerably simplified way.
Last updated:  2022-09-19
Hybrid scalar/vector implementations of Keccak and SPHINCS+ on AArch64
Hanno Becker and Matthias J. Kannwischer
This paper presents two new techniques for the fast implementation of the Keccak permutation on the A-profile of the Arm architecture: First, the elimination of explicit rotations in the Keccak permutation through Barrel shifting, applicable to scalar AArch64 implementations of Keccak-f1600. Second, the construction of hybrid implementations concurrently leveraging both the scalar and the Neon instruction sets of AArch64. The resulting performance improvements are demonstrated in the example of the hash-based signature scheme SPHINCS+, one of the recently announced winners of the NIST post-quantum cryptography project: We achieve up to 1.89× performance improvements compared to the state of the art. Our implementations target the Arm Cortex-{A55,A510,A78,A710,X1,X2} processors common in client devices such as mobile phones.
Last updated:  2022-09-19
Data Protection Law and Multi-Party Computation: Applications to Information Exchange between Law Enforcement Agencies
Amos Treiber, Dirk Müllmann, Thomas Schneider, and Indra Spiecker genannt Döhmann
Pushes for increased power of Law Enforcement (LE) for data retention and centralized storage result in legal challenges with data protection law and courts - and possible violations of the right to privacy. This is motivated by a desire for better cooperation and exchange between LE Agencies (LEAs), which is difficult due to data protection regulations, was identified as a main factor of major public security failures, and is a frequent criticism of LE. Secure Multi-Party Computation (MPC) is often seen as a technological means to solve privacy conflicts where actors want to exchange and analyze data that needs to be protected due to data protection laws. In this interdisciplinary work, we investigate the problem of private information exchange between LEAs from both a legal and technical angle. We give a legal analysis of secret-sharing based MPC techniques in general and, as a particular application scenario, consider the case of matching LE databases for lawful information exchange between LEAs. We propose a system for lawful information exchange between LEAs using MPC and private set intersection and show its feasibility by giving a legal analysis for data protection and a technical analysis for workload complexity. Towards practicality, we present insights from qualitative feedback gathered within exchanges with a major European LEA.
Last updated:  2022-09-19
Continued Fractions Applied to a Family of RSA-like Cryptosystems
George Teseleanu and Paul Cotan
Let $N=pq$ be the product of two balanced prime numbers $p$ and $q$. Murru and Saettone presented in 2017 an interesting RSA-like cryptosystem that uses the key equation $ed - k (p^2+p+1)(q^2+q+1) = 1$, instead of the classical RSA key equation $ed - k (p-1)(q-1) = 1$. The authors claimed that their scheme is immune to Wiener's continued fraction attack. Unfortunately, Nitaj \emph{et. al.} developed exactly such an attack. In this paper, we introduce a family of RSA-like encryption schemes that uses the key equation $ed - k [(p^n-1)(q^n-1)]/[(p-1)(q-1)] = 1$, where $n>1$ is an integer. Then, we show that regardless of the choice of $n$, there exists an attack based on continued fractions that recovers the secret exponent.
Last updated:  2022-09-19
Sherlock Holmes Zero-Knowledge Protocols
George Teseleanu
We present two simple zero knowledge interactive proofs that can be instantiated with many of the standard decisional or computational hardness assumptions. Compared with traditional zero knowledge proofs, in our protocols the verifiers starts first, by emitting a challenge, and then the prover answers the challenge.
Last updated:  2022-09-19
Improving Bounds on Elliptic Curve Hidden Number Problem for ECDH Key Exchange
Jun Xu, Santanu Sarkar, Huaxiong Wang, and Lei Hu
Elliptic Curve Hidden Number Problem (EC-HNP) was first introduced by Boneh, Halevi and Howgrave-Graham at Asiacrypt 2001. To rigorously assess the bit security of the Diffie--Hellman key exchange with elliptic curves (ECDH), the Diffie--Hellman variant of EC-HNP, regarded as an elliptic curve analogy of the Hidden Number Problem (HNP), was presented at PKC 2017. This variant can also be used for practical cryptanalysis of ECDH key exchange in the situation of side-channel attacks. In this paper, we revisit the Coppersmith method for solving the involved modular multivariate polynomials in the Diffie--Hellman variant of EC-HNP and demonstrate that, for any given positive integer $d$, a given sufficiently large prime $p$, and a fixed elliptic curve over the prime field $\mathbb{F}_p$, if there is an oracle that outputs about $\frac{1}{d+1}$ of the most (least) significant bits of the $x$-coordinate of the ECDH key, then one can give a heuristic algorithm to compute all the bits within polynomial time in $\log_2 p$. When $d>1$, the heuristic result $\frac{1}{d+1}$ significantly outperforms both the rigorous bound $\frac{5}{6}$ and heuristic bound $\frac{1}{2}$. Due to the heuristics involved in the Coppersmith method, we do not get the ECDH bit security on a fixed curve. However, we experimentally verify the effectiveness of the heuristics on NIST curves for small dimension lattices.
Last updated:  2022-09-19
Secure Quantum Bit Commitment
Ping Wang, Yiting Su, and Fangguo Zhang
Bit commitment (BC) is one of the most important fundamental protocols in secure multi-party computation. However, it is generally believed that unconditionally secure bit commitment is impossible even with quantum resources. In this paper, we design a secure non-interactive bit commitment protocol by exploiting the no-communication theorem of the quantum entangled states, whose security relies on the indistinguishability of whether the Bell states are measured or not. The proposed quantum bit commitment (QBC) is secure against classical adversaries with unlimited computing power, and the probability of a successful attack by quantum adversaries decreases exponentially as $n$ (the number of qubits in a group) increases.
Last updated:  2022-09-18
On the Worst-Case Inefficiency of CGKA
Alexander Bienstock, Yevgeniy Dodis, Sanjam Garg, Garrison Grogan, Mohammad Hajiabadi, and Paul Rösler
Continuous Group Key Agreement (CGKA) is the basis of modern Secure Group Messaging (SGM) protocols. At a high level, a CGKA protocol enables a group of users to continuously compute a shared (evolving) secret while members of the group add new members, remove other existing members, and perform state updates. The state updates allow CGKA to offer desirable security features such as forward secrecy and post-compromise security. CGKA is regarded as a practical primitive in the real-world. Indeed, there is an IETF Messaging Layer Security (MLS) working group devoted to developing a standard for SGM protocols, including the CGKA protocol at their core. Though known CGKA protocols seem to perform relatively well when considering natural sequences of performed group operations, there are no formal guarantees on their efficiency, other than the $O(n)$ bound which can be achieved by trivial protocols, where $n$ is the number of group numbers. In this context, we ask the following questions and provide negative answers. 1. Can we have CGKA protocols that are efficient in the worst case? We start by answering this basic question in the negative. First, we show that a natural primitive that we call Compact Key Exchange (CKE) is at the core of CGKA, and thus tightly captures CGKA's worst-case communication cost. Intuitively, CKE requires that: first, $n$ users non-interactively generate key pairs and broadcast their public keys, then, some other special user securely communicates to these $n$ users a shared key. Next, we show that CKE with communication cost $o(n)$ by the special user cannot be realized in a black-box manner from public-key encryption, thus implying the same for CGKA, where $n$ is the corresponding number of group members. Surprisingly, this impossibility holds even in an offline setting, where parties have access to the sequence of group operations in advance. 2. Can we realize one CGKA protocol that works as well as possible in all cases? Here again, we present negative evidence showing that no such protocol based on black-box use of public-key encryption exists. Specifically, we show two distributions over sequences of group operations such that no CGKA protocol obtains optimal communication costs on both sequences.
Last updated:  2022-09-18
Rate-1 Non-Interactive Arguments for Batch-NP and Applications
Lalita Devadas, Rishab Goyal, Yael Kalai, and Vinod Vaikuntanathan
We present a rate-$1$ construction of a publicly verifiable non-interactive argument system for batch-$\mathsf{NP}$ (also called a BARG), under the LWE assumption. Namely, a proof corresponding to a batch of $k$ NP statements each with an $m$-bit witness, has size $m + \mathsf{poly}(\lambda,\log k)$. In contrast, prior work either relied on non-standard knowledge assumptions, or produced proofs of size $m \cdot \mathsf{poly}(\lambda,\log k)$ (Choudhuri, Jain, and Jin, STOC 2021, following Kalai, Paneth, and Yang 2019). We show how to use our rate-$1$ BARG scheme to obtain the following results, all under the LWE assumption: - A multi-hop BARG scheme for $\mathsf{NP}$. - A multi-hop aggregate signature scheme (in the standard model). - An incrementally verifiable computation (IVC) scheme for arbitrary $T$-time deterministic computations with proof size $\mathsf{poly}(\lambda,\log T)$. Prior to this work, multi-hop BARGs were only known under non-standard knowledge assumptions or in the random oracle model; aggregate signatures were only known under indistinguishability obfuscation (and RSA) or in the random oracle model; IVC schemes with proofs of size $\mathsf{poly}(\lambda,T^{\epsilon})$ were known under a bilinear map assumption, and with proofs of size $\mathsf{poly}(\lambda,\log T)$ under non-standard knowledge assumptions or in the random oracle model.
Last updated:  2022-09-17
QCCA-Secure Generic Transformations in the Quantum Random Oracle Model
Tianshu Shan, Jiangxia Ge, and Rui Xue
The post-quantum security of cryptographic systems assumes that the quantum adversary only receives the classical result of computations with the secret key. Furthermore, if the adversary is able to obtain a superposition state of the result, it is unknown whether the post-quantum secure schemes still remain secure. In this paper, we formalize one class of public-key encryption schemes, named oracle-masked schemes, relative to random oracles. For each oracle-masked scheme, we design a preimage extraction procedure and prove that it simulates the quantum decryption oracle with a certain loss. We also observe that the implementation of the preimage extraction procedure for some oracle-masked schemes does not need to take the secret key as input. This contributes to the IND-qCCA security proof of these schemes in the quantum random oracle model (QROM). As an application, we prove the IND-qCCA security of schemes obtained by the Fujisaki-Okamoto (FO) transformation and REACT transformation in the QROM, respectively. Notably, our security reduction for FO transformation is tighter than the reduction given by Zhandry (Crypto 2019).
Last updated:  2022-09-17
Towards Tight Security Bounds for OMAC, XCBC and TMAC
Soumya Chattopadhyay, Ashwin Jha, and Mridul Nandi
OMAC --- a single-keyed variant of CBC-MAC by Iwata and Kurosawa --- is a widely used and standardized (NIST FIPS 800-38B, ISO/IEC 29167-10:2017) message authentication code (MAC) algorithm. The best security bound for OMAC is due to Nandi who proved that OMAC's pseudorandom function (PRF) advantage is upper bounded by $ O(q^2\ell/2^n) $, where $ n $, $ q $, and $ \ell $, denote the block size of the underlying block cipher, the number of queries, and the maximum permissible query length (in terms of $ n $-bit blocks), respectively. In contrast, there is no attack with matching lower bound. Indeed, the best known attack on OMAC is the folklore birthday attack achieving a lower bound of $ \Omega(q^2/2^n) $. In this work, we close this gap for a large range of message lengths. Specifically, we show that OMAC's PRF security is upper bounded by $ O(q^2/2^n + q\ell^2/2^n)$. In practical terms, this means that for a $ 128 $-bit block cipher, and message lengths up to $ 64 $ Gigabyte, OMAC can process up to $ 2^{64} $ messages before rekeying (same as the birthday bound). In comparison, the previous bound only allows $ 2^{48} $ messages. As a side-effect of our proof technique, we also derive similar tight security bounds for XCBC (by Black and Rogaway) and TMAC (by Kurosawa and Iwata). As a direct consequence of this work, we have established tight security bounds (in a wide range of $\ell$) for all the CBC-MAC variants, except for the original CBC-MAC.
Last updated:  2022-09-20
Forward-Secure Encryption with Fast Forwarding
Yevgeniy Dodis, Daniel Jost, and Harish Karthikeyan
Forward-secure encryption (FSE) allows communicating parties to refresh their keys across epochs, in a way that compromising the current secret key leaves all prior encrypted communication secure. We investigate a novel dimension in the design of FSE schemes: fast-forwarding (FF). This refers to the ability of a stale communication party, that is "stuck" in an old epoch, to efficiently "catch up" to the newest state, and frequently arises in practice. While this dimension was not explicitly considered in prior work, we observe that one can augment prior FSEs -- both in symmetric- and public-key settings -- to support fast-forwarding which is sublinear in the number of epochs. However, the resulting schemes have disadvantages: the symmetric-key scheme is a security parameter slower than any conventional stream cipher, while the public-key scheme inherits the inefficiencies of the HIBE-based forward-secure PKE. To address these inefficiencies, we look at the common real-life situation which we call the bulletin board model, where communicating parties rely on some infrastructure -- such as an application provider -- to help them store and deliver ciphertexts to each other. We then define and construct FF-FSE in the bulletin board model, which addresses the above-mentioned disadvantages. In particular, * Our FF-stream-cipher in the bulletin-board model has: (a) constant state size; (b) constant normal (no fast-forward) operation; and (c) logarithmic fast-forward property. This essentially matches the efficiency of non-fast-forwardable stream ciphers, at the cost of constant communication complexity with the bulletin board per update. * Our public-key FF-FSE avoids HIBE-based techniques by instead using so-called updatable public-key encryption (UPKE), introduced in several recent works (and more efficient than public-key FSEs). Our UPKE-based scheme uses a novel type of "update graph" that we construct in this work. Our graph has constant in-degree, logarithmic diameter, and logarithmic "cut property" which is essential for the efficiency of our schemes. Combined with recent UPKE schemes, we get two FF-FSEs in the bulletin board model, under the DDH and the LWE assumptions.
Last updated:  2022-09-16
The Abe-Okamoto Partially Blind Signature Scheme Revisited
Julia Kastner, Julian Loss, and Jiayu Xu
Partially blind signatures, an extension of ordinary blind signatures, are a primitive with wide applications in e-cash and electronic voting. One of the most efficient schemes to date is the one by Abe and Okamoto (CRYPTO 2000), whose underlying idea - the OR-proof technique - has served as the basis for several works. We point out several subtle flaws in the original proof of security, and provide a new detailed and rigorous proof, achieving similar bounds as the original work. We believe our insights on the proof strategy will find useful in the security analyses of other OR-proof-based schemes.
Last updated:  2022-09-16
Continuously Non-Malleable Codes against Bounded-Depth Tampering
Gianluca Brian, Sebastian Faust, Elena Micheli, and Daniele Venturi
Non-malleable codes (Dziembowski, Pietrzak and Wichs, ICS 2010 & JACM 2018) allow protecting arbitrary cryptographic primitives against related-key attacks (RKAs). Even when using codes that are guaranteed to be non-malleable against a single tampering attempt, one obtains RKA security against poly-many tampering attacks at the price of assuming perfect memory erasures. In contrast, continuously non-malleable codes (Faust, Mukherjee, Nielsen and Venturi, TCC 2014) do not suffer from this limitation, as the non-malleability guarantee holds against poly-many tampering attempts. Unfortunately, there are only a handful of constructions of continuously non-malleable codes, while standard non-malleable codes are known for a large variety of tampering families including, e.g., NC0 and decision-tree tampering, AC0, and recently even bounded polynomial-depth tampering. We change this state of affairs by providing the first constructions of continuously non-malleable codes in the following natural settings: - Against decision-tree tampering, where, in each tampering attempt, every bit of the tampered codeword can be set arbitrarily after adaptively reading up to $d$ locations within the input codeword. Our scheme is in the plain model, can be instantiated assuming the existence of one-way functions, and tolerates tampering by decision trees of depth $d = O(n^{1/8})$, where $n$ is the length of the codeword. Notably, this class includes NC0. - Against bounded polynomial-depth tampering, where in each tampering attempt the adversary can select any tampering function that can be computed by a circuit of bounded polynomial depth (and unbounded polynomial size). Our scheme is in the common reference string model, and can be instantiated assuming the existence of time-lock puzzles and simulation-extractable (succinct) non-interactive zero-knowledge proofs.
Last updated:  2022-09-16
Group Action Key Encapsulation and Non-Interactive Key Exchange in the QROM
Julien Duman, Dominik Hartmann, Eike Kiltz, Sabrina Kunzweiler, Jonas Lehmann, and Doreen Riepel
In the context of quantum-resistant cryptography, cryptographic group actions offer an abstraction of isogeny-based cryptography in the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) setting. In this work, we revisit the security of two previously proposed natural protocols: the Group Action Hashed ElGamal key encapsulation mechanism (GA-HEG KEM) and the Group Action Hashed Diffie-Hellman non-interactive key-exchange (GA-HDH NIKE) protocol. The latter protocol has already been considered to be used in practical protocols such as Post-Quantum WireGuard (S&P '21) and OPTLS (CCS '20). We prove that active security of the two protocols in the Quantum Random Oracle Model (QROM) inherently relies on very strong variants of the Group Action Strong CDH problem, where the adversary is given arbitrary quantum access to a DDH oracle. That is, quantum accessible Strong CDH assumptions are not only sufficient but also necessary to prove active security of the GA-HEG KEM and the GA-HDH NIKE protocols. Furthermore, we propose variants of the protocols with QROM security from the classical Strong CDH assumption, i.e., CDH with classical access to the DDH oracle. Our first variant uses key confirmation and can therefore only be applied in the KEM setting. Our second but considerably less efficient variant is based on the twinning technique by Cash et al. (EUROCRYPT '08) and in particular yields the first actively secure isogeny-based NIKE with QROM security from the standard CDH assumption.
Last updated:  2022-09-16
Cumulatively All-Lossy-But-One Trapdoor Functions from Standard Assumptions
Benoît Libert, Ky Nguyen, and Alain Passelègue
Chakraborty, Prabhakaran, and Wichs (PKC'20) recently introduced a new tag-based variant of lossy trapdoor functions, termed cumulatively all-lossy-but-one trapdoor functions (CALBO-TDFs). Informally, CALBO-TDFs allow defining a public tag-based function with a (computationally hidden) special tag, such that the function is lossy for all tags except when the special secret tag is used. In the latter case, the function becomes injective and efficiently invertible using a secret trapdoor. This notion has been used to obtain advanced constructions of signatures with strong guarantees against leakage and tampering, and also by Dodis, Vaikunthanathan, and Wichs (EUROCRYPT'20) to obtain constructions of randomness extractors with extractor-dependent sources. While these applications are motivated by practical considerations, the only known instantiation of CALBO-TDFs so far relies on the existence of indistinguishability obfuscation. In this paper, we propose the first two instantiations of CALBO-TDFs based on standard assumptions. Our constructions are based on the LWE assumption with a sub-exponential approximation factor and on the DCR assumption, respectively, and circumvent the use of indistinguishability obfuscation by relying on lossy modes and trapdoor mechanisms enabled by these assumptions.
Last updated:  2022-09-16
SCARF: A Low-Latency Block Cipher for Secure Cache-Randomization
Federico Canale, Tim Güneysu, Gregor Leander, Jan Thoma, Yosuke Todo, and Rei Ueno
Show abstract
Randomized cache architectures have proven to significantly increase the complexity of contention-based cache side channel attacks and therefore pre\-sent an important building block for side channel secure microarchitectures. By randomizing the address-to-cache-index mapping, attackers can no longer trivially construct minimal eviction sets which are fundamental for contention-based cache attacks. At the same time, randomized caches maintain the flexibility of traditional caches, making them broadly applicable across various CPU-types. This is a major advantage over cache partitioning approaches. A large variety of randomized cache architectures has been proposed. However, the actual randomization function received little attention and is often neglected in these proposals. Since the randomization operates directly on the critical path of the cache lookup, the function needs to have extremely low latency. At the same time, attackers must not be able to bypass the randomization which would nullify the security benefit of the randomized mapping. In this paper we propose \cipher (\underline{S}ecure \underline{CA}che \underline{R}andomization \underline{F}unction), the first dedicated cache randomization cipher which achieves low latency and is cryptographically secure in the cache attacker model. The design methodology for this dedicated cache cipher enters new territory in the field of block ciphers with a small 10-bit block length and heavy key-dependency in few rounds.
Last updated:  2022-09-16
How to Sample a Discrete Gaussian (and more) from a Random Oracle
George Lu and Brent Waters
The random oracle methodology is central to the design of many practical cryptosystems. A common challenge faced in several systems is the need to have a random oracle that outputs from a structured distribution $\mathcal{D}$, even though most heuristic implementations such as SHA-3 are best suited for outputting bitstrings. Our work explores the problem of sampling from discrete Gaussian (and related) distributions in a manner that they can be programmed into random oracles. We make the following contributions: -We provide a definitional framework for our results. We say that a sampling algorithm $\mathsf{Sample}$ for a distribution is explainable if there exists an algorithm $\mathsf{Explain}$ where, for a $x$ in the domain, we have that $\mathsf{Explain}(x) \rightarrow r \in \{0,1\}^n$ such that $\mathsf{Sample}(r)=x$. Moreover, if $x$ is sampled from $\mathcal{D}$ the explained distribution is statistically close to choosing $r$ uniformly at random. We consider a variant of this definition that allows the statistical closeness to be a "precision parameter'' given to the $\mathsf{Explain}$ algorithm. We show that sampling algorithms which satisfy our `explainability' property can be programmed as a random oracle. -We provide a simple algorithm for explaining \emph{any} sampling algorithm that works over distributions with polynomial sized ranges. This includes discrete Gaussians with small standard deviations. -We show how to transform a (not necessarily explainable) sampling algorithm $\mathsf{Sample}$ for a distribution into a new $\mathsf{Sample}'$ that is explainable. The requirements for doing this is that (1) the probability density function is efficiently computable (2) it is possible to efficiently uniformly sample from all elements that have a probability density above a given threshold $p$, showing the equivalence of random oracles to these distributions and random oracles to uniform bitstrings. This includes a large class of distributions, including all discrete Gaussians. -A potential drawback of the previous approach is that the transformation requires an additional computation of the density function. We provide a more customized approach that shows the Miccancio-Walter discrete Gaussian sampler is explainable as is. This suggests that other discrete Gaussian samplers in a similar vein might also be explainable as is.
Last updated:  2022-09-16
Algebraic Relation of Three MinRank Algebraic Modelings
Hao Guo and Jintai Ding
We give algebraic relations among equations of three algebraic modelings for MinRank problem: support minors modeling, Kipnis–Shamir modeling and minors modeling.
Last updated:  2022-09-15
Hybrid Post-Quantum Signatures in Hardware Security Keys
Diana Ghinea, Fabian Kaczmarczyck, Jennifer Pullman, Julien Cretin, Stefan Kölbl, Rafael Misoczki, Jean-Michel Picod, Luca Invernizzi, and Elie Bursztein
Recent advances in quantum computing are increasingly jeopardizing the security of cryptosystems currently in widespread use, such as RSA or elliptic-curve signatures. To address this threat, researchers and standardization institutes have accelerated the transition to quantum-resistant cryptosystems, collectively known as Post-Quantum Cryptography (PQC). These PQC schemes present new challenges due to their larger memory and computational footprints and their higher chance of latent vulnerabilities. In this work, we address these challenges by introducing a scheme to upgrade the digital signatures used by security keys to PQC, focusing on both its theoretical and practical aspects. Specifically, we introduce a hybrid digital signature scheme based on two building blocks: a classically-secure scheme, ECDSA, and a post-quantum secure one, Dilithium. Our hybrid scheme maintains the guarantees of each underlying building block even if the other one is broken, thus being resistant to classical and quantum attacks. Additionally, our hybrid scheme ensures that an adversary cannot derive ECDSA or Dilithium signatures that this authentication protocol considers valid. On the practical aspect, we experimentally show that our hybrid signature scheme can successfully execute on current security keys, even though secure PQC schemes are known to require substantial resources. We publish an open-source implementation of our scheme at so that other researchers can reproduce our results on a nRF52840 development kit.
Last updated:  2022-09-15
From Plaintext-extractability to IND-CCA Security
Ehsan Ebrahimi
We say a public-key encryption is plaintext-extractable in the random oracle model if there exists an algorithm that given access to all inputs/outputs queries to the random oracles can simulate the decryption oracle. We argue that plaintext-extractability is enough to show the indistinguishably under chosen ciphertext attack (IND-CCA) of OAEP+ transform (Shoup, Crypto 2001) when the underlying trapdoor permutation is one-way. We extend the result to the quantum random oracle model (QROM) and show that OAEP+ is IND-CCA secure in QROM if the underlying trapdoor permutation is quantum one-way.
Last updated:  2022-09-15
Efficient Proofs of Software Exploitability for Real-world Processors
Matthew Green, Mathias Hall-Andersen, Eric Hennenfent, Gabriel Kaptchuk, Benjamin Perez, and Gijs Van Laer
We consider the problem of proving in zero-knowledge the existence of vulnerabilities in executables compiled to run on real-world processors. We demonstrate that it is practical to prove knowledge of real exploits for real-world processor architectures without the need for source code and without limiting our consideration to narrow vulnerability classes. To achieve this, we devise a novel circuit compiler and a toolchain that produces highly optimized, non-interactive zero-knowledge proofs for programs executed on the MSP430, an ISA commonly used in embedded hardware. Our toolchain employs a highly optimized circuit compiler and a number of novel optimizations to construct efficient proofs for program binaries. To demonstrate the capability of our system, we test our toolchain by constructing proofs for challenges in the Microcorruption capture the flag exercises.
Last updated:  2022-09-15
Homomorphic Encryption on GPU
Ali Şah Özcan, Can Ayduman, Enes Recep Türkoğlu, and Erkay Savaş
Homomorphic encryption (HE) is a cryptosystem that allows secure processing of encrypted data. One of the most popular HE schemes is the Brakerski-Fan-Vercauteren (BFV), which supports somewhat (SWHE) and fully homomorphic encryption (FHE). Since overly involved arithmetic operations of HE schemes are amenable to concurrent computation, GPU devices can be instrumental in facilitating the practical use of HE in real world applications thanks to their superior parallel processing capacity. This paper presents an optimized and highly parallelized GPU library to accelerate the BFV scheme. This library includes state-of-the-art implementations of Number Theoretic Transform (NTT) and inverse NTT that minimize the GPU kernel function calls. It makes an efficient use of the GPU memory hierarchy and computes 128 NTT operations for ring dimension of $2^{14}$ only in $176.1~\mu s$ on RTX~3060Ti GPU. To the best of our knowlede, this is the fastest implementation in the literature. The library also improves the performance of the homomorphic operations of the BFV scheme. Although the library can be independently used, it is also fully integrated with the Microsoft SEAL library, which is a well-known HE library that also implements the BFV scheme. For one ciphertext multiplication, for the ring dimension $2^{14}$ and the modulus bit size of $438$, our GPU implementation offers $\mathbf{63.4}$ times speedup over the SEAL library running on a high-end CPU. The library compares favorably with other state-of-the-art GPU implementations of NTT and the BFV operations. Finally, we implement a privacy-preserving application that classifies encrpyted genome data for tumor types and achieve speedups of $42.98$ and $5.7$ over a CPU implementations using single and 16 threads, respectively. Our results indicate that GPU implementations can facilitate the deployment of homomorphic cryptographic libraries in real world privacy preserving applications.
Last updated:  2022-09-15
Multi-User Security of the Sum of Truncated Random Permutations (Full Version)
Wonseok Choi, Hwigyeom Kim, Jooyoung Lee, and Yeongmin Lee
For several decades, constructing pseudorandom functions from pseudorandom permutations, so-called Luby-Rackoff backward construction, has been a popular cryptographic problem. Two methods are well-known and comprehensively studied for this problem: summing two random permutations and truncating partial bits of the output from a random permutation. In this paper, by combining both summation and truncation, we propose new Luby-Rackoff backward constructions, dubbed SaT1 and SaT2, respectively. SaT2 is obtained by partially truncating output bits from the sum of two independent random permutations, and SaT1 is its single permutation-based variant using domain separation. The distinguishing advantage against SaT1 and SaT2 is upper bounded by O(\sqrt{\mu q_max}/2^{n-0.5m}) and O({\sqrt{\mu}q_max^1.5}/2^{2n-0.5m}), respectively, in the multi-user setting, where n is the size of the underlying permutation, m is the output size of the construction, \mu is the number of users, and q_max is the maximum number of queries per user. We also prove the distinguishing advantage against a variant of XORP[3]~(studied by Bhattacharya and Nandi at Asiacrypt 2021) using independent permutations, dubbed SoP3-2, is upper bounded by O(\sqrt{\mu} q_max^2}/2^{2.5n})$. In the multi-user setting with \mu = O(2^{n-m}), a truncated random permutation provides only the birthday bound security, while SaT1 and SaT2 are fully secure, i.e., allowing O(2^n) queries for each user. It is the same security level as XORP[3] using three permutation calls, while SaT1 and SaT2 need only two permutation calls.
Last updated:  2022-09-14
Permissionless Clock Synchronization with Public Setup
Juan Garay, Aggelos Kiayias, and Yu Shen
The permissionless clock synchronization problem asks how it is possible for a population of parties to maintain a system-wide synchronized clock, while their participation rate fluctuates --- possibly very widely --- over time. The underlying assumption is that parties experience the passage of time with roughly the same speed, but however they may disengage and engage with the protocol following arbitrary (and even chosen adversarially) participation patterns. This (classical) problem has received renewed attention due to the advent of blockchain protocols, and recently it has been solved in the setting of proof of stake, i.e., when parties are assumed to have access to a trusted PKI setup [Badertscher et al., Eurocrypt ’21]. In this work, we present the first proof-of-work (PoW)-based permissionless clock synchronization protocol. Our construction assumes a public setup (e.g., a CRS) and relies on an honest majority of computational power that, for the first time, is described in a fine-grain timing model that does not utilize a global clock that exports the current time to all parties. As a secondary result of independent interest, our protocol gives rise to the first PoW-based ledger consensus protocol that does not rely on an external clock for the time-stamping of transactions and adjustment of the PoW difficulty.
Last updated:  2022-09-14
Anonymous Random Allocation and Its Applications
Azam Soleimanian
Random Allocation -the random assignment of the data to the parties- is a well-studied topic in the analysis of medical or judicial data, and the context of resource distribution. Random allocation reduces the chance of bias or corruption in the relevant applications, which makes the results more reliable. This is done by preventing a special or pre-planned assignment of the data to accommodate the assessment toward the desired results. This paper provides the first formal syntax and security notion of a random allocation scheme. Based on our new security notions of anonymity, confidentiality, and data-integrity, random allocation can cover more applications such as the distributed audit system where the confidentiality of data and the anonymity of auditors are of paramount importance. Our protocol allows the parties to stay anonymous during the concurrent executions of the protocol even if they have revealed themselves at a certain execution. The revelation property gives the possibility to the parties to claim certain advantages/faults at the end of a protocol-execution (without breaking the data-privacy or anonymity in other protocol-executions). We instantiate our syntax and prove the security based on simple cryptographic components and assumptions such as the Diffie-Hellman assumption, in the random oracle model.
Last updated:  2022-09-21
Stretching Cube Attacks: Improved Methods to Recover Massive Superpolies
Jiahui He, Kai Hu, Bart Preneel, and Meiqin Wang
Cube attacks exploit the algebraic properties of symmetric ciphers by recovering a special polynomial, the superpoly, and subsequently the secret key. When the algebraic normal forms of the corresponding Boolean functions are not available, the division property based approach allows to recover the exact superpoly in a clever way. However, the computational cost to recover the superpoly becomes prohibitive as the number of rounds of the cipher increases. For example, the nested monomial predictions (NMP) proposed at ASIACRYPT 2021 stuck at round 845 for Trivium. To alleviate the bottleneck of the NMP technique, i.e., the unsolvable model due to the excessive number of monomial trails, we shift our focus to the so-called valuable terms of a specific middle round that contribute to the superpoly. Two new techniques are introduced, namely, Non-zero Bit-based Division Property (NBDP) and Core Monomial Prediction (CMP), both of which result in a simpler MILP model compared to the MILP model of MP. It can be shown that the CMP technique offers a substantial improvement over the monomial prediction technique in terms of computational complexity of recovering valuable terms. Combining the divide-and-conquer strategy with these two new techniques, we catch the valuable terms more effectively and thus avoid wasting computational resources on intermediate terms contributing nothing to the superpoly. As an illustration of the power of our techniques, we apply our framework to Trivium, Grain, Kreyvium and Acorn. As a result, the computational cost of earlier attacks can be significantly reduced and the exact ANFs of the superpolies for 846-, 847- and 848-round Trivium, 192-round Grain, 895-round Kreyvium and 776-round Acorn can be recovered in practical time, even though the superpoly of 848-round Trivium contains over 500 million terms; this corresponds to respectively 3, 1, 1 and 1 rounds more than the previous best results. Moreover, by investigating the internal properties of Möbius transformation, we show how to perform key recovery using superpolies involving full key bits, which leads to the best key recovery attacks on the targeted ciphers.
Last updated:  2022-09-14
Privacy-Preserving Authenticated Key Exchange in the Standard Model
You Lyu, Shengli Liu, Shuai Han, and Dawu Gu
Privacy-Preserving Authenticated Key Exchange (PPAKE) provides protection both for the session keys and the identity information of the involved parties. In this paper, we introduce the concept of robustness into PPAKE. Robustness enables each user to confirm whether itself is the target recipient of the first round message in the protocol. With the help of robustness, a PPAKE protocol can successfully avoid the heavy redundant communications and computations caused by the ambiguity of communicants in the existing PPAKE, especially in broadcast channels. We propose a generic construction of robust PPAKE from key encapsulation mechanism (KEM), digital signature (SIG), message authentication code (MAC), pseudo-random generator (PRG) and symmetric encryption (SE). By instantiating KEM, MAC, PRG from the DDH assumption and SIG from the CDH assumption, we obtain a specific robust PPAKE scheme in the standard model, which enjoys forward security for session keys, explicit authentication and forward privacy for user identities. Thanks to the robustness of our PPAKE, the number of broadcast messages per run and the computational complexity per user are constant, and in particular, independent of the number of users in the system.
Last updated:  2022-09-21
A summary on the FRI low degree test
Ulrich Haböck
This document is an informal summary on the FRI low degree test [BSBHR18a], [BSCI+20], and DEEP algebraic linking from [BSGKS20]. Based on its most recent soundness analysis [BSCI+20], we discuss parameter settings for practical security levels, how FRI is turned into a polynomial commitment scheme, and the soundness of DEEP sampling in the list decoding regime. In particular, we illustrate the DEEP method applied to proving satisfiability of algebraic intermediate representations and prove a soundness error bound which slightly improves the one in [Sta21].
Last updated:  2022-09-13
Continuous Authentication in Secure Messaging
Benjamin Dowling, Felix Günther, and Alexandre Poirrier
Secure messaging schemes such as the Signal protocol rely on out-of-band channels to verify the authenticity of long-running communication. Such out-of-band checks however are only rarely actually performed by users in practice. In this paper, we propose a new method for performing continuous authentication during a secure messaging session, without the need for an out-of-band channel. Leveraging the users' long-term secrets, our Authentication Steps extension guarantees authenticity as long as long-term secrets are not compromised, strengthening Signal's post-compromise security. Our mechanism further allows to detect a potential compromise of long-term secrets after the fact via an out-of-band channel. Our protocol comes with a novel, formal security definition capturing continuous authentication, a general construction for Signal-like protocols, and a security proof for the proposed instantiation. We further provide a prototype implementation which seamlessly integrates on top of the official Signal Java library, together with bandwidth and storage overhead benchmarks.
Last updated:  2022-09-13
Updatable NIZKs from Non-Interactive Zaps
Karim Baghery and Navid Ghaedi Bardeh
In ASIACRYPT 2016, Bellare, Fuchsbauer, and Scafuro studied the security of NIZK arguments under subverted Structured Reference String (SRS) and presented some positive and negative results. In their best positive result, they showed that by defining an SRS as a tuple of knowledge assumption in bilinear groups (e.g. $g^a, g^b, g^{ab}$), and then using a Non-Interactive (NI) zap to prove that either there is a witness for the statement $\mathsf{x}$ or one knows the trapdoor of SRS (e.g. $a$ or $b$), one can build NIZK arguments that can achieve soundness and $\textit{subversion zero-knowledge}$ (zero-knowledge without trusting a third party; Sub-ZK). In this paper, we expand their idea and use NI zaps (of knowledge) to build NIZK arguments (of knowledge) with $\textit{updatable}$, $\textit{universal}$, and $\textit{succinct}$ SRS. To this end, we first show that their proposed sound and Sub-ZK NIZK argument can also achieve $\textit{updatable}$ soundness, which is a more desired notion than the plain soundness. Updatable soundness allows the verifier to update the SRS one time and bypass the need for a trusted third party. Then, we show that using a similar OR language, given a NI zap (of knowledge) and a $\textit{key-updatable}$ signature scheme, one can build NIZK arguments that can achieve Sub-ZK and $\textit{updatable}$ simulation soundness (resp. $\textit{updatable}$ simulation extractability). The proposed constructions are the first NIZK arguments that have updatable and succinct SRS, and do not require a random oracle. Our instantiations show that in the resulting NIZK arguments the computational cost for the parties to verify/update the SRS is negligible, namely, a few exponentiations and pairing checks. The run times of the prover and verifier, as well as the size of the proof, are asymptotically the same as those of the underlying NI zap.
Last updated:  2022-09-13
Nostradamus goes Quantum
Barbara Jiabao Benedikt, Marc Fischlin, and Moritz Huppert
In the Nostradamus attack, introduced by Kelsey and Kohno (Eurocrypt 2006), the adversary has to commit to a hash value y of an iterated hash function H such that, when later given a message prefix P, the adversary is able to find a suitable "suffix explanation" S with H(P||S)=y. Kelsey and Kohno show a herding attack with $2^{2n/3}$ evaluations of the compression function of H (with n bits output and state), locating the attack between preimage attacks and collision search in terms of complexity. Here we investigate the security of Nostradamus attacks for quantum adversaries. We present a quantum herding algorithm for the Nostradamus problem making approximately $\sqrt[3]{n}\cdot 2^{3n/7}$ compression function evaluations, significantly improving over the classical bound. We also prove that quantum herding attacks cannot do better than $2^{3n/7}$ evaluations for random compression functions, showing that our algorithm is (essentially) optimal. We also discuss a slightly less tight bound of roughly $2^{3n/7-s}$ for general Nostradamus attacks against random compression functions, where s is the maximal block length of the adversarially chosen suffix S.
Last updated:  2022-09-14
VoteXX: A Solution to Improper Influence in Voter-Verifiable Elections
David Chaum, Richard T. Carback, Jeremy Clark, Chao Liu, Mahdi Nejadgholi, Bart Preneel, Alan T. Sherman, Mario Yaksetig, Zeyuan Yin, Filip Zagórski, and Bingsheng Zhang
We solve a long-standing challenge to the integrity of votes cast without the supervision of a voting booth: “improper influence,” which we define as any combination of vote buying and voter coercion. Our approach allows each voter, or their trusted agent(s), to cancel their vote in a way that is unstoppable, irrevocable, and forever unattributable to the voter. In particular, our approach enhances security of online, remote, public-sector elections, for which there is a growing need and the threat of improper influence is most acute. In this extended abstract, we introduce the new approach, compare it with previous methods, and concisely summarize the protocols. In our full paper, we give detailed cryptographic protocols, show how they can be applied to several voting settings, describe our implementation in a full voting system called VoteXX, and provide UC proofs. Our system protects against the strongest adversary considered in prior related work and is suitable for widespread use in public elections.
Last updated:  2022-09-13
Arithmetization of Functional Program Execution via Interaction Nets in Halo 2
Anthony Hart
We sketch a method for creating a zero-knowledge proof of knowledge for the correct execution of a program within a model of higher-order, recursive, purely functional programming by leveraging Halo 2. To our knowledge, this is the first ZKP for general purpose computation based on purely functional computation. This is an attractive alternative to using a von Neumann architecture based zero-knowledge virtual machine for verified computing of functional programs, as compilation will be more direct, making it more easily verifiable and potentially more efficient. Interaction nets are a natural setting for recursive, higher-order functional programming where all computation steps are linear and local. Interaction nets are graphs and traces for such programs are hyper-graphs. Correctness of a trace is a simple syntactic check over the structure of the trace represented as a hyper-graph. We reformulate this syntactic check as a Halo 2 circuit which is universal over all traces.
Last updated:  2022-09-13
On the Field-Based Division Property: Applications to MiMC, Feistel MiMC and GMiMC (Full Version)
Jiamin Cui, Kai Hu, Meiqin Wang, and Puwen Wei
Recent practical applications using advanced cryptographic protocols such as multi-party computations (MPC) and zero-knowledge proofs (ZKP) have prompted a range of novel symmetric primitives described over large finite fields, characterized as arithmetization-oriented AO ciphers. Such designs, aiming to minimize the number of multiplications over fields, have a high risk of being vulnerable to algebraic attacks, especially to the higher-order differential attack. Thus, it is significant to carefully evaluate the growth of their algebraic degree. However, the degree estimation for AO ciphers has been a challenge for cryptanalysts due to the lack of general and accurate methods. In this paper, we extend the division property, a state-of-the-art framework for finding the upper bound of the algebraic degree over binary fields, to the scope of $\mathbb{F}_{2^n}$. It is a generic method to detect the algebraic degree for AO ciphers, even applicable to Feistel ciphers which have no better bounds than the trivial exponential one. In this general division property, our idea is to evaluate whether the polynomial representation of a block cipher contains some specific monomials. With a deep investigation of the arithmetical feature, we introduce the propagation rules of monomials for field-based operations, which can be efficiently modeled using the bit-vector theory of SMT. Then the new searching tool for degree estimation can be constructed due to the relationship between the algebraic degree and the exponents of monomials. We apply our new framework to some important AO ciphers, including Feistel MiMC, GMiMC, and MiMC. For Feistel MiMC, we show that the algebraic degree grows significantly slower than the native exponential bound. For the first time, we present a secret-key higher-order differential distinguisher for up to 124 rounds, much better than the 83-round distinguisher for Feistel MiMC permutation proposed at CRYPTO 2020. We also exhibit a full-round zero-sum distinguisher with a data complexity of $2^{251}$. Our method can be further extended for the general Feistel structure with more branches and exhibit higher-order differential distinguishers against the practical instance of GMiMC for up to 50 rounds. For MiMC in SP-networks, our results correspond to the exact algebraic degree proved by Bouvier et al. We also point out that the number of rounds in MiMC's specification is not sufficient to guarantee the security against the higher-order differential attack for MiMC-like schemes with different exponents. The investigation of different exponents provides some guidance on the cipher design.
Last updated:  2022-09-13
Puncturable Key Wrapping and Its Applications
Matilda Backendal, Felix Günther, and Kenneth G. Paterson
We introduce puncturable key wrapping (PKW), a new cryptographic primitive that supports fine-grained forward security properties in symmetric key hierarchies. We develop syntax and security definitions, along with provably secure constructions for PKW from simpler components (AEAD schemes and puncturable PRFs). We show how PKW can be applied in two distinct scenarios. First, we show how to use PKW to achieve forward security for TLS 1.3 0-RTT session resumption, even when the server's long-term key for generating session tickets gets compromised. This extends and corrects a recent work of Aviram, Gellert, and Jager (Journal of Cryptology, 2021). Second, we show how to use PKW to build a protected file storage system with file shredding, wherein a client can outsource encrypted files to a potentially malicious or corrupted cloud server whilst achieving strong forward-security guarantees, relying only on local key updates.
Last updated:  2022-09-13
Notes on Reusable Garbling
Hu Yupu, Dong Siyue, Wang Baocang, and Liu Jun
Garbling is a cryptographic primitive which has many applications. It is mainly used for scenes of limited authority, such as multi-party computation (MPC), attribute-based encryption (ABE), functional encryption (FE), indistinguishability obfuscation (IO), etc. Garbling schemes before 2013 are of one-time garbling. Goldwasser et al and Agrawal presented a reusable garbling scheme, which made use of a symmetric encryption scheme and an FE scheme as the components. In this paper we discuss the validity and the efficiency of reusable garbling scheme. We present the following three notes on the scheme. (1) Reusable garbling scheme does not provide new applications, and it is still a one-time garbling scheme. (2) Even reusable garbling scheme is taken as a one-time garbling scheme, sometimes it is not usable. More detailedly, it can only be used for Basic Scene 2, and cannot be used for Basic Scene 1. For example, it cannot be used for MPC. (3) Even reusable garbling scheme is taken as a one-time garbling scheme used for Basic Scene 2, there is no evidence to show that its efficiency is better than a former one-time garbling scheme.
Last updated:  2022-09-13
Attaining GOD Beyond Honest Majority With Friends and Foes
Aditya Hegde, Nishat Koti, Varsha Bhat Kukkala, Shravani Patil, Arpita Patra, and Protik Paul
In the classical notion of multiparty computation (MPC), an honest party learning private inputs of others, either as a part of protocol specification or due to a malicious party's unspecified messages, is not considered a potential breach. Several works in the literature exploit this seemingly minor loophole to achieve the strongest security of guaranteed output delivery via a trusted third party, which nullifies the purpose of MPC. Alon et al. (CRYPTO 2020) presented the notion of Friends and Foes ($\mathtt{FaF}$) security, which accounts for such undesired leakage towards honest parties by modelling them as semi-honest (friends) who do not collude with malicious parties (foes). With real-world applications in mind, it's more realistic to assume parties are semi-honest rather than completely honest, hence it is imperative to design efficient protocols conforming to the $\mathtt{FaF}$ security model. Our contributions are not only motivated by the practical viewpoint, but also consider the theoretical aspects of $\mathtt{FaF}$ security. We prove the necessity of semi-honest oblivious transfer for $\mathtt{FaF}$-secure protocols with optimal resiliency. On the practical side, we present QuadSquad, a ring-based 4PC protocol, which achieves fairness and GOD in the $\mathtt{FaF}$ model, with an optimal corruption of $1$ malicious and $1$ semi-honest party. QuadSquad is, to the best of our knowledge, the first practically efficient $\mathtt{FaF}$ secure protocol with optimal resiliency. Its performance is comparable to the state-of-the-art dishonest majority protocols while improving the security guarantee from abort to fairness and GOD. Further, QuadSquad elevates the security by tackling a stronger adversarial model over the state-of-the-art honest-majority protocols, while offering a comparable performance for the input-dependent computation. We corroborate these claims by benchmarking the performance of QuadSquad. We also consider the application of liquidity matching that deals with highly sensitive financial transaction data, where $\mathtt{FaF}$ security is apt. We design a range of $\mathtt{FaF}$ secure building blocks to securely realize liquidity matching as well as other popular applications such as privacy-preserving machine learning (PPML). Inclusion of these blocks makes QuadSquad a comprehensive framework.
Last updated:  2022-09-13
On the Optimal Communication Complexity of Error-Correcting Multi-Server PIR
Reo Eriguchi, Kaoru Kurosawa, and Koji Nuida
An $\ell$-server Private Information Retrieval (PIR) scheme enables a client to retrieve a data item from a database replicated among $\ell$ servers while hiding the identity of the item. It is called $b$-error-correcting if a client can correctly compute the data item even in the presence of $b$ malicious servers. It is known that $b$-error correction is possible if and only if $\ell>2b$. In this paper, we first prove that if error correction is perfect, i.e., the client always corrects errors, the minimum communication cost of $b$-error-correcting $\ell$-server PIR is asymptotically equal to that of regular $(\ell-2b)$-server PIR as a function of the database size $n$. Secondly, we formalize a relaxed notion of statistical $b$-error-correcting PIR, which allows non-zero failure probability. We show that as a function of $n$, the minimum communication cost of statistical $b$-error-correcting $\ell$-server PIR is asymptotically equal to that of regular $(\ell-b)$-server one, which is at most that of $(\ell-2b)$-server one. Our main technical contribution is a generic construction of statistical $b$-error-correcting $\ell$-server PIR for any $\ell>2b$ from regular $(\ell-b)$-server PIR. We can therefore reduce the problem of determining the optimal communication complexity of error-correcting PIR to determining that of regular PIR. In particular, our construction instantiated with the state-of-the-art PIR schemes and the previous lower bound for single-server PIR result in a separation in terms of communication cost between perfect and statistical error correction for any $\ell>2b$.
Last updated:  2022-09-21
Accountable Light Client Systems for PoS Blockchains
Oana Ciobotaru, Fatemeh Shirazi, Alistair Stewart, and Sergey Vasilyev
A major challenge for blockchain interoperability is having an on-chain light client protocol that is both efficient and secure. We present a protocol that provides short proofs about the state of a decentralised consensus protocol while being able to detect misbehaving parties. To do this naively, a verifier would need to maintain an updated list of all participants' public keys which makes the corresponding proofs long. In general, existing solutions either lack accountability or are not efficient. We define and design a committee key scheme with short proofs that do not include any of the individual participants' public keys in plain. Our committee key scheme, in turn, uses a custom designed SNARK which has a fast prover time. Moreover, using our committee key scheme, we define and design an accountable light client system as the main cryptographic core for building bridges between proof of stake blockchains. Finally, we implement a prototype of our custom SNARK for which we provide benchmarks.
Last updated:  2022-09-12
The Pseudorandom Oracle Model and Ideal Obfuscation
Aayush Jain, Huijia Lin, Ji Luo, and Daniel Wichs
Show abstract
We introduce a new idealized model of hash functions, which we refer to as the *pseudorandom oracle* (PrO) model. Intuitively, it allows us to model cryptosystems that use the code of a hash function in a non-black-box way. Formally, we model hash functions via a combination of a pseudorandom function (PRF) family and an ideal oracle. A user can initialize the hash function by choosing a PRF key $k$ and the oracle maps it to a public handle $h$. Given the handle $h$ and some input $x$, the oracle will recover the PRF key $k$ and evaluate the PRF on $x$. A user who chooses the PRF key $k$ therefore has a complete description of the hash function and can use its code in non-black-box constructions, while an adversary, who just gets the handle $h$, only has black-box access to the hash function via the oracle. As our main result, we show how to construct ideal obfuscation in the PrO model, starting from functional encryption (FE), which in turn can be based on well-studied polynomial hardness assumptions. In contrast, we know that ideal obfuscation cannot be instantiated in the basic random oracle model under any assumptions. We believe our result gives a heuristic justification for the following: (1) most natural security goals implied by ideal obfuscation are achievable in the real world; (2) we can construct obfuscation from FE with polynomial security loss. We also discuss how to interpret our result in the PrO model as a construction of ideal obfuscation using simple hardware tokens or as a way to bootstrap ideal obfuscation for PRFs to that for all functions.
Last updated:  2022-09-15
On Module Unique-SVP and NTRU
Joël Felderhoff, Alice Pellet-Mary, and Damien Stehlé
The NTRU problem can be viewed as an instance of finding a short non-zero vector in a lattice, under the promise that it contains an exceptionally short vector. Further, the lattice under scope has the structure of a rank-2 module over the ring of integers of a number field. Let us refer to this problem as the module unique Shortest Vector Problem,or mod-uSVP for short. We exhibit two reductions that together provide evidence the NTRU problem is not just a particular case of mod-uSVP, but representative of it from a computational perspective. First, we reduce worst-case mod-uSVP to worst-case NTRU. For this, we rely on an oracle for id-SVP, the problem of finding short non-zero vectors in ideal lattices. Using the worst-case id-SVP to worst-case NTRU reduction from Pellet-Mary and Stehlé [ASIACRYPT'21],this shows that worst-case NTRU is equivalent to worst-case mod-uSVP. Second, we give a random self-reduction for mod-uSVP. We put forward a distribution D over mod-uSVP instances such that solving mod-uSVP with a non-negligible probability for samples from D allows to solve mod-uSVP in the worst-case. With the first result, this gives a reduction from worst-case mod-uSVP to an average-case version of NTRU where the NTRU instance distribution is inherited from D. This worst-case to average-case reduction requires an oracle for id-SVP.
Last updated:  2022-09-12
Disorientation faults in CSIDH
Gustavo Banegas, Juliane Krämer, Tanja Lange, Michael Meyer, Lorenz Panny, Krijn Reijnders, Jana Sotáková, and Monika Trimoska
We investigate a new class of fault-injection attacks against the CSIDH family of cryptographic group actions. Our disorientation attacks effectively flip the direction of some isogeny steps. We achieve this by faulting a specific subroutine, connected to the Legendre symbol or Elligator computations performed during the evaluation of the group action. These subroutines are present in almost all known CSIDH implementations. Post-processing a set of faulty samples allows us to infer constraints on the secret key. The details are implementation specific, but we show that in many cases, it is possible to recover the full secret key with only a modest number of successful fault injections and modest computational resources. We provide full details for attacking the original CSIDH proof-of-concept software as well as the CTIDH constant-time implementation. Finally, we present a set of lightweight countermeasures against the attack and discuss their security.
Last updated:  2022-09-12
Consistent, Efficient and Leakage-Model Free Mutual Information Estimation
Arnab Roy, Aakash Chowdhury, and Elisabeth Oswald
Show abstract
The mutual information between the observable device leakage and the unknown key is a key metric in the context of side channel attacks, evaluations, and countermeasures. Estimating this mutual information has been a problem and was addressed in several recent contributions. We explain why previous work has ended up in a "catch-22'' and we show how to avoid this situation by using a leakage model free estimation approach based on a recently discovered, consistent mutual information estimator. Our work demonstrates that mutual information estimation in the side channel setting can be done extremely efficiently (even in a multivariate setting), with strong mathematical guarantees, without the need for an explicit device leakage model, discretisation, or assumptions about the nature of the device leakage.
Last updated:  2022-09-11
SEEK: model extraction attack against hybrid secure inference protocols
Si Chen and Junfeng Fan
Security concerns about a machine learning model used in a prediction-as-a-service include the privacy of the model, the query and the result. Secure inference solutions based on homomorphic encryption (HE) and/or multiparty computation (MPC) have been developed to protect all the sensitive information. One of the most efficient type of solution utilizes HE for linear layers, and MPC for non-linear layers. However, for such hybrid protocols with semi-honest security, an adversary can malleate the intermediate features in the inference process, and extract model information more effectively than methods against inference service in plaintext. In this paper, we propose SEEK, a general extraction method for hybrid secure inference services outputing only class labels. This method can extract each layer of the target model independently, and is not affected by the depth of the model. For ResNet-18, SEEK can extract a parameter with less than 50 queries on average, with average error less than $0.03\%$.
Last updated:  2022-09-13
Structure Evaluation of AES-like Ciphers against Mixture Differential Cryptanalysis
Xiaofeng Xie and Tian Tian
In ASIACRYPT 2017, Rønjom et al. analyzed AES with yoyo attack. Inspired by their 4-round AES distinguisher, Grassi proposed the mixture differential cryptanalysis as well as a key recovery attack on 5-round AES, which was shown to be better than the classical square attack in computation complexity. After that, Bardeh et al. combined the exchange attack with the 4-round mixture differential distinguisher of AES, leading to the first secret-key chosen plaintext distinguisher for 6-round AES. Unlike the attack on 5-round AES, the result of 6-round key-recovery attack on AES has extremely large complexity, which implies the weakness of mixture difference to a certain extent. Our work aims at evaluating the security of AES-like ciphers against mixture differential cryptanalysis. We propose a new structure called a boomerang struncture and illustrate that a differential distinguisher of a boomerang struncture just corresponds to a mixture differential distinguisher for AES-like ciphers. Based on the boomerang structure, it is shown that the mixture differential cryptanalysis is not suitable to be applied to AES-like ciphers with high round number. In specific, we associate the primitive index with our framework built on the boomerang structure and give the upper bound for the length of mixture differentials with probability 1 on AES-like ciphers. It can be directly deduced from our framework that there is no mixture differential distinguisher for 6-round AES.
Last updated:  2022-09-16
To Be, or Not to Be Stateful: Post-Quantum Secure Boot using Hash-Based Signatures
Alexander Wagner, Felix Oberhansl, and Marc Schink
While research in post-quantum cryptography (PQC) has gained significant momentum, it is only slowly adopted for real-world products. This is largely due to concerns about practicability and maturity. The secure boot process of embedded devices is one s- cenario where such restraints can result in fundamental security problems. In this work, we present a flexible hardware/software co-design for hash-based signature (HBS) schemes which enables the move to a post-quantum secure boot today. These signature schemes stand out due to their straightforward security proofs and are on the fast track to standardisation. In contrast to previous works, we exploit the performance intensive similarities of the s- tateful LMS and XMSS schemes as well as the stateless SPHINCS+ scheme. Thus, we enable designers to use a stateful or stateless scheme depending on the constraints of each individual application. To show the feasibility of our approach, we compare our results with hardware accelerated implementations of classical asymmetric algorithms. Further, we lay out the usage of different HBS schemes during the boot process. We compare different schemes, show the importance of parameter choices, and demonstrate the performance gain with different levels of hardware acceleration.
Last updated:  2022-09-11
On Squaring Modulo Mersenne Numbers
David Naccache and Ofer Yifrach-Stav
During the design of a new primitive inspired by Squash we accidentally stumbled on the observation described in this note. Let $n$ be a $k$-bit Mersenne number whose factors are unknown. Consider an $\ell$-bit secret number $x=2^{k/2}a+b$. We observe that there are parameter configurations where a chunk of the value $b^2$ is leaked even if $k<2\ell$. This observation does not endanger any known scheme and in particular not Squash.
Last updated:  2022-09-11
Embedded Identity Traceable Identity-Based IPFE from Pairings and Lattices
Subhranil Dutta, Tapas Pal, Amit Kumar Singh, and Sourav Mukhopadhyay
We present the first fully collusion resistant traitor tracing (TT) scheme for identity-based inner product functional encryption (IBIPFE) that directly traces user identities through an efficient tracing procedure. We name such a scheme as embedded identity traceable IBIPFE (EI-TIBIPFE), where secret keys and ciphertexts are computed for vectors u and v respectively. Additionally, each secret key is associated with a user identification information tuple (i , id, gid) that specifies user index i , user identity id and an identity gid of a group to which the user belongs. The ciphertexts are generated under a group identity gid′ so that decryption recovers the inner product between the vectors u and v if the user is a member of the group gid′, i.e., gid = gid′. Suppose some users linked to a particular group team up and create a pirate decoder that is capable of decrypting the content of the group, then the tracing algorithm extracts at least one id from the team given black-box access to the decoder. In prior works, such TT schemes are built for usual public key encryptions. The only existing TIPFE scheme proposed by Do, Phan, and Pointcheval [CT-RSA’20] can trace user indices but not the actual identities. Moreover, their scheme achieves selective security and private traceability, meaning that it is only the trusted authority that is able to trace user indices. In this work, we present the following TT schemes with varying parameters and levels of security: (1) We generically construct EI-TIBIPFE assuming the existence of IBIPFE. The scheme preserves the security level of the underlying IBIPFE. (2) We build an adaptively secure EI-TIPFE scheme from bilinear maps. Note that EI-TIPFE is a particular case of EI-TIBIPFE, which does not consider group identities. (3) Next, we construct a selectively secure EI-TIBIPFE from bilinear maps. As an intermediate step, we design the first IBIPFE scheme based on a target group assumption in the standard model. (4) Finally, we provide a generic construction of selectively secure EI-TIBIPFE from lattices, namely under the standard Learning With Errors assumption. Our pairing-based schemes support public traceability and the ciphertext size grows with $\sqrt{n}$, whereas in the IBIPFE and lattice-based ones, it grows linearly with n. The main technical difficulty is designing such an advanced TT scheme for an IBIPFE that is beyond IPFE and more suitable for real-life applications.
Last updated:  2022-09-10
A Deep Neural Differential Distinguisher for ARX based Block Cipher
Debranjan Pal, Upasana Mandal, Mainak Chaudhury, Abhijit Das, and Dipanwita Roy Chowdhury
Over the last few years, deep learning is becoming the most trending topic for the classical cryptanalysis of block ciphers. Differential cryptanalysis is one of the primary and potent attacks on block ciphers. Here we apply deep learning techniques to model differential cryptanalysis more easily. In this paper, we report a generic tool using deep neural classifier that assists to find differential distinguishers for block ciphers with reduced round. We apply this approach for the differential cryptanalysis of ARX- based encryption schemes HIGHT, LEA, and SPARX. The result shows that our deep learning based distinguishers work with high accuracy for 14-round HIGHT, 13-Round LEA and 11-round SPARX. We also achieve an improvement of the lower bound of data complexity for these three ARX based ciphers.
Last updated:  2022-09-10
Multi-Authority ABE from Lattices without Random Oracles
Brent Waters, Hoeteck Wee, and David J. Wu
Attribute-based encryption (ABE) extends public-key encryption to enable fine-grained control to encrypted data. However, this comes at the cost of needing a central trusted authority to issue decryption keys. A multi-authority ABE (MA-ABE) scheme decentralizes ABE and allows anyone to serve as an authority. Existing constructions of MA-ABE only achieve security in the random oracle model. In this work, we develop new techniques for constructing MA-ABE for the class of subset policies (which captures policies such as conjunctions and DNF formulas) whose security can be based in the plain model without random oracles. We achieve this by relying on the recently-proposed "evasive" learning with errors (LWE) assumption by Wee (EUROCRYPT 2022) and Tsabury (CRYPTO 2022). Along the way, we also provide a modular view of the MA-ABE scheme for DNF formulas by Datta et al. (EUROCRYPT 2021) in the random oracle model. We formalize this via a general version of a related-trapdoor LWE assumption by Brakerski and Vaikuntanathan (ITCS 2022), which can in turn be reduced to the plain LWE assumption. As a corollary, we also obtain an MA-ABE scheme for subset policies from plain LWE with a polynomial modulus-to-noise ratio in the random oracle model. This improves upon the Datta et al. construction which relied on LWE with a sub-exponential modulus-to-noise ratio. Moreover, we are optimistic that the generalized related-trapdoor LWE assumption will also be useful for analyzing the security of other lattice-based constructions.
Last updated:  2022-09-10
Knowledge Encryption and Its Applications to Simulatable Protocols With Low Round-Complexity
Yi Deng and Xinxuan Zhang
We introduce a new notion of public key encryption, knowledge encryption, for which its ciphertexts can be reduced to the public-key, i.e., any algorithm that can break the ciphertext indistinguishability can be used to extract the (partial) secret key. We show that knowledge encryption can be built solely on any two-round oblivious transfer with game-based security, which are known based on various standard (polynomial-hardness) assumptions, such as the DDH, the Quadratic($N^{th}$) Residuosity or the LWE assumption. We use knowledge encryption to construct the first three-round (weakly) simulatable oblivious transfer. This protocol satisfies (fully) simulatable security for the receiver, and weakly simulatable security ($(T, \epsilon)$-simulatability) for the sender in the following sense: for any polynomial $T$ and any inverse polynomial $\epsilon$, there exists an efficient simulator such that the distinguishing gap of any distinguisher of size less than $T$ is at most $\epsilon$. Equipped with these tools, we construct a variety of fundamental cryptographic protocols with low round-complexity, assuming only the existence of two-round oblivious transfer with game-based security. These protocols include three-round delayed-input weak zero knowledge argument, three-round weakly secure two-party computation, three-round concurrent weak zero knowledge in the BPK model, and a two-round commitment with weak security under selective opening attack. These results improve upon the assumptions required by the previous constructions. Furthermore, all our protocols enjoy the above $(T, \epsilon)$-simulatability (stronger than the distinguisher-dependent simulatability), and are quasi-polynomial time simulatable under the same (polynomial hardness) assumption.
Last updated:  2022-09-09
(Augmented) Broadcast Encryption from Identity Based Encryption with Wildcard
Anaïs Barthoulot, Olivier Blazy, and Sébastien Canard
Several broadcast encryption (BE) constructions have been proposed since Fiat and Naor introduced the concept, some achieving short parameters size while others achieve better security. Since 1994, a lot of alternatives to BE have moreover been additionally proposed, such as the broadcast and trace (BT) primitive which is a combination of broadcast encryption and traitor tracing. Among the other variants of BE, the notion of augmented BE (AugBE), introduced by Boneh and Waters in 2006, corresponds to a BE scheme with the particularity that the encryption algorithm takes an index as an additional parameter. If an AugBE scheme is both message and index hiding, it has been proved that it can generically be used to construct a secure BT scheme. Hence, any new result related to the former gives an improvement to the latter. In this paper, we first show that both BE and AugBE can be obtained by using an identity-based encryption scheme with wildcard (WIBE). We also introduce the new notion of anonymous AugBE, where the used users set is hidden, and prove that it implies index hiding. We then provide two different WIBE constructions. The first one has constant size ciphertext and used to construct a new constant size ciphertext BE scheme with adaptive CPA security, in the standard model (under the $\SXDH{}$ assumption). The second WIBE provides pattern-hiding, a new definition we introduced, and serves as a basis for the first anonymous AugBE scheme (and subsequently a BT scheme since our scheme is also index hiding by nature) in the literature, with adaptive security in the standard model (under the $\XDLin{}$ assumption).
Last updated:  2022-09-09
A New Framework for Quantum Oblivious Transfer
Amit Agarwal, James Bartusek, Dakshita Khurana, and Nishant Kumar
We present a new template for building oblivious transfer from quantum information that we call the ``fixed basis'' framework. Our framework departs from prior work (eg., Crepeau and Kilian, FOCS '88) by fixing the correct choice of measurement basis used by each player, except for some hidden trap qubits that are intentionally measured in a conjugate basis. We instantiate this template in the quantum random oracle model (QROM) to obtain simple protocols that implement, with security against malicious adversaries: - Non-interactive random-input bit OT in a model where parties share EPR pairs a priori. - Two-round random-input bit OT without setup, obtained by showing that the protocol above remains secure even if the (potentially malicious) OT receiver sets up the EPR pairs. - Three-round chosen-input string OT from BB84 states without entanglement or setup. This improves upon natural variations of the CK88 template that require at least five rounds. Along the way, we develop technical tools that may be of independent interest. We prove that natural functions like XOR enable seedless randomness extraction from certain quantum sources of entropy. We also use idealized (i.e. extractable and equivocal) bit commitments, which we obtain by proving security of simple and efficient constructions in the QROM.
Last updated:  2022-09-09
Statistical Security in Two-Party Computation Revisited
Saikrishna Badrinarayanan, Sikhar Patranabis, and Pratik Sarkar
We present a new framework for building round-optimal one-sided statistically secure two party computation (2PC) protocols in the plain model. We demonstrate that a relatively weak notion of oblivious transfer (OT), namely a three round elementary oblivious transfer $\textsf{eOT}$ with statistical receiver privacy, along with a non-interactive commitment scheme suffices to build a one-sided statistically secure two party computation protocol with black-box simulation. Our framework enables the first instantiations of round-optimal one-sided statistically secure 2PC protocols from the CDH assumption and certain families of isogeny-based assumptions. As part of our compiler, we introduce the following new one-sided statistically secure primitives in the pre-processing model that might also be of independent interest: 1. Three round statistically sender private random-OT where only the last OT message depends on the receiver's choice bit and the sender receives random outputs generated by the protocol. 2. Four round delayed-input statistically sender private conditional disclosure of secrets where the first two rounds of the protocol are independent of the inputs of the parties. The above primitives are directly constructed from $\textsf{eOT}$ and hence we obtain their instantiations from the same set of assumptions as our 2PC.
Last updated:  2022-09-09
CSI-SharK: CSI-FiSh with Sharing-friendly Keys
Shahla Atapoor, Karim Baghery, Daniele Cozzo, and Robi Pedersen
CSI-FiSh is one of the most efficient isogeny-based signature schemes, which is proven to be secure in the Quantum Random Oracle Model (QROM). However, there is a bottleneck in CSI-FiSh in the threshold setting, which is that its public key needs to be generated by using $k-1$ secret keys. This leads to very inefficient threshold key generation protocols and also forces the parties to store $k-1$ secret shares. We present CSI-SharK, a new variant of $\textit{CSI}$-FiSh that has more $\textit{Shar}$ing-friendly $\textit{K}$eys and is as efficient as the original scheme. This is accomplished by modifying the public key of the ID protocol, used in the original CSI-FiSh, to the equal length Structured Public Key (SPK), generated by a $\textit{single}$ secret key, and then proving that the modified ID protocol and the resulting signature scheme remain secure in the QROM. We translate existing CSI-FiSh-based threshold signatures and Distributed Key Generation (DKG) protocols to the CSI-SharK setting. We find that DKG schemes based on CSI-SharK outperform the state-of-the-art actively secure DKG protocols from the literature by a factor of about $3$, while also strongly reducing the communication cost between the parties. We also uncover and discuss a flaw in the key generation of the actively secure CSI-FiSh based threshold signature scheme $\textit{Sashimi}$, that can prevent parties from signing. Finally, we discuss how (distributed) key generation and signature schemes in the isogeny setting are strongly parallelizable and we show that by using $C$ independent CPU threads, the total runtime of such schemes can basically be reduced by a factor $C$. As multiple threads are standard in modern CPU architecture, this parallelizability is a strong incentive towards using isogeny-based (distributed) key generation and signature schemes in practical scenarios.
Last updated:  2022-09-09
High-order masking of NTRU
Jean-Sebastien Coron, François Gérard, Matthias Trannoy, and Rina Zeitoun
The main protection against side-channel attacks consists in computing every function with multiple shares via the masking countermeasure. While the masking countermeasure was originally developed for securing block-ciphers such as AES, the protection of lattice-based cryptosystems is often more challenging, because of the diversity of the underlying algorithms. In this paper, we introduce new gadgets for the high-order masking of the NTRU cryptosystem, with security proofs in the classical ISW probing model. We then describe the first fully masked implementation of the NTRU Key Encapsulation Mechanism submitted to NIST, including the key generation. To assess the practicality of our countermeasures, we provide a concrete implementation on ARM Cortex-M3 architecture, and eventually a t-test leakage evaluation.
Last updated:  2022-09-09
Strongly Anonymous Ratcheted Key Exchange
Benjamin Dowling, Eduard Hauck, Doreen Riepel, and Paul Rösler
Anonymity is an (abstract) security goal that is especially important to threatened user groups. Therefore, widely deployed communication protocols implement various measures to hide different types of information (i.e., metadata) about their users. Before actually defining anonymity, we consider an attack vector about which targeted user groups can feel concerned: continuous, temporary exposure of their secrets. Examples for this attack vector include intentionally planted viruses on victims' devices, as well as physical access when their users are detained. Inspired by Signal's Double-Ratchet Algorithm, Ratcheted (or Continuous) Key Exchange (RKE) is a novel class of protocols that increase confidentiality and authenticity guarantees against temporary exposure of user secrets. For this, an RKE regularly renews user secrets such that the damage due to past and future exposures is minimized; this is called Post-Compromise Security and Forward-Secrecy, respectively. With this work, we are the first to leverage the strength of RKE for achieving strong anonymity guarantees under temporary exposure of user secrets. We extend existing definitions for RKE to capture attacks that interrelate ciphertexts, seen on the network, with secrets, exposed from users' devices. Although, at first glance, strong authenticity (and confidentiality) conflicts with strong anonymity, our anonymity definition is as strong as possible without diminishing other goals. We build strongly anonymity-, authenticity-, and confidentiality-preserving RKE and, along the way, develop new tools with applicability beyond our specific use-case: Updatable and Randomizable Signatures as well as Updatable and Randomizable Public Key Encryption. For both new primitives, we build efficient constructions.
Last updated:  2022-09-09
Adversarial Correctness and Privacy for Probabilistic Data Structures
Mia Filić, Kenneth G. Paterson, Anupama Unnikrishnan, and Fernando Virdia
We study the security of Probabilistic Data Structures (PDS) for handling Approximate Membership Queries (AMQ); prominent examples of AMQ-PDS are Bloom and Cuckoo filters. AMQ-PDS are increasingly being deployed in environments where adversaries can gain benefit from carefully selecting inputs, for example to increase the false positive rate of an AMQ-PDS. They are also being used in settings where the inputs are sensitive and should remain private in the face of adversaries who can access an AMQ-PDS through an API or who can learn its internal state by compromising the system running the AMQ-PDS. We develop simulation-based security definitions that speak to correctness and privacy of AMQ-PDS. Our definitions are general and apply to a broad range of adversarial settings. We use our defi- nitions to analyse the behaviour of both Bloom filters and insertion- only Cuckoo filters. We show that these AMQ-PDS can be provably protected through replacement or composition of hash functions with keyed pseudorandom functions in their construction. We also examine the practical impact on storage size and computation of providing secure instances of Bloom and insertion-only Cuckoo filters.
Last updated:  2022-09-09
PEA: Practical private epistasis analysis using MPC
Kay Hamacher, Tobias Kussel, Thomas Schneider, and Oleksandr Tkachenko
Due to the significant drop in prices for genome sequencing in the last decade, genome databases were constantly growing. This enabled genome analyses such as Genome-Wide Association Studies (GWAS) that study associations between a gene and a disease and allow to improve medical treatment. However, GWAS fails at the analysis of complex diseases caused by non-linear gene-gene interactions such as sporadic breast cancer or type 2 diabetes. Epistasis Analysis (EA) is a more powerful approach that complements GWAS and considers non-linear interactions between multiple parts of the genome and environment. Statistical genome analyses require large, well-curated genomic datasets, which are difficult to obtain. Hence, the aggregation of multiple databases is often necessary, but the sharing of genomic data raises severe privacy concerns and is subject to extensive regulations (e.g., GDPR or HIPAA), requiring further privacy protection for collaborative analyses. Although there has been work on private GWAS, there was a lack of attention to Private EA (PEA). In this work, we design the first secure and accurate PEA protocol, with security against passive adversaries. Our efficient PEA protocol consists of two subprotocols: (1) (optional) feature selection for filtering noisy features to reduce the input size for better efficiency and (2) finding relevant associations. For feature selection, we design two protocols based on Secure Multi-Party Computation (MPC) for Relief-F and TuRF. For finding associations, we design an MPC protocol for Multifactor Dimensionality Reduction (MDR). Our private MDR protocol is based on two novel, efficient building blocks, arithmetic greater than and arithmetic swap, which may be of independent interest. This approach omits the need for expensive conversions between sharing types in private MDR and reduces the communication by two orders of magnitude compared to a naïve design using garbled circuits. Our private MDR protocol runs in (extrapolated) three days on a practical database with 10,000 features for all two mutually combined features, i.e., considering about 50 million combinations.
Last updated:  2022-09-09
On digital signatures based on isomorphism problems: QROM security and ring signatures
Zhili Chen, Dung Hoang Duong, Ngoc Tuong Nguyen, Youming Qiao, Willy Susilo, and Gang Tang
At Eurocrypt 2022, Tang et al proposed a practical digital signature scheme in the context of post-quantum cryptography. The construction of that scheme is based on the assumed hardness of the alternating trilinear form equivalence problem (ATFE), the Goldreich-Micali-Widgerson (GMW) zero-knowledge protocol for graph isomorphism, and the Fiat-Shamir (FS) transformation. We refer to that scheme as the ATFE-GMW-FS scheme. The security of the ATFE-GMW-FS scheme was only proved in the random oracle model (ROM), and its security in the quantum random oracle model (QROM) was left as an open problem. In this paper, we study the ATFE-GMW-FS scheme from two perspectives, namely the QROM security and (linkable) ring signature schemes. First, we provide two approaches of proving its QROM security, based on the perfect unique response property and lossy identification schemes, respectively. Second, we design (linkable) ring signatures based on the ATFE-GMW-FS scheme, inspired by a recent result of Beullens, Katsumata and Pintore (Asiacrypt 20) on isogeny-based cryptography.
Last updated:  2022-09-09
Towards a Fast and Efficient Hardware Implementation of HQC
Sanjay Deshpande, Mamuri Nawan, Kashif Nawaz, Jakub Szefer, and Chuanqi Xu
This work presents a hardware design for constant-time implementation of the HQC (Hamming Quasi-Cyclic) code-based key encapsulation mechanism. HQC has been selected for the fourth-round of NIST's Post-Quantum Cryptography standardization process and this work presents first, hand-optimized design of HQC key generation, encapsulation, and decapsulation written in Verilog targeting implementation on FPGAs. The three modules further share a common SHAKE256 hash module to reduce area overhead. All the hardware modules are parametrizable at compile time so that designs for the different security levels can be easily generated. The architecture of the hardware modules includes novel, dual clock domain design, allowing the common SHAKE module to run at slower clock speed compared to the rest of the design, while other faster modules run at their optimal clock rate. The design currently outperforms the other hardware designs for HQC, and many of the fourth-round Post-Quantum Cryptography standardization process, with one of the best time-area products as well. For the dual clock design targeting lowest security level, we show that the HQC design can perform key generation in 0.12ms, encapsulation in 0.30ms, and decapsulation in 0.43ms when synthesized for an Xilinx Artix 7 FPGA. The performance can be increased even further at the cost of resources by increasing the level of parallelism, e.g. by having parallel polynomial multiplication modules in the encrypt module, or including even more clock domains, one for each of the main modules. The presented design will further be made available under open-source license.
Last updated:  2022-09-09
Machine-Checked Proofs of Privacy Against Malicious Boards for Selene & Co
Constantin Cătălin Drăgan, François Dupressoir, Ehsan Estaji, Kristian Gjøsteen, Thomas Haines, Peter Y. A. Ryan, Peter B. Rønne, and Morten Rotvold Solberg
Privacy is a notoriously difficult property to achieve in complicated systems and especially in electronic voting schemes. Moreover, electronic voting schemes is a class of systems that require very high assurance. The literature contains a number of ballot privacy definitions along with security proofs for common systems. Some machine-checked security proofs have also appeared. We define a new ballot privacy notion that captures a larger class of voting schemes. This notion improves on the state of the art by taking into account that verification in many schemes will happen or must happen after the tally has been published, not before as in previous definitions. As a case study we give a machine-checked proof of privacy for Selene, which is a remote electronic voting scheme which offers an attractive mix of security properties and usability. Prior to our work, the computational privacy of Selene has never been formally verified. Finally, we also prove that MiniVoting and Belenios satisfies our definition.
Last updated:  2022-09-09
On the computational hardness needed for quantum cryptography
Zvika Brakerski, Ran Canetti, and Luowen Qian
In the classical model of computation, it is well established that one-way functions (OWF) are essential for almost every computational cryptographic application. In the quantum setting, however, OWFs appear not to be essential (Kretschmer 2021; Ananth et al., Morimae and Yamakawa 2022), and the question of whether a minimal primitive exists remains open. We consider EFI pairs — efficiently samplable, statistically far but computationally indistinguishable pairs of distributions. Building on the work of Yan (2022) which shows equivalence between EFI pairs and statistical commitment schemes, we show that EFI pairs are necessary and sufficient for a large class of quantum-cryptographic applications. Specifically, while it was known how to construct commitments schemes, oblivious transfer, and general secure multiparty computation from any EFI, we show how to construct EFI pairs from minimalistic versions of each one of these primitives. We also construct from EFI quantum computational zero knowledge (𝖰𝖢𝖹𝖪) proofs for all of 𝖰𝖨𝖯, and construct EFI pairs from essentially any non-trivial 𝖰𝖢𝖹𝖪. This suggests that, for much of quantum cryptography, EFI pairs play a similar role to that played by OWFs in the classical setting: they are simple to describe, essential, and also serve as a linchpin for demonstrating equivalence between primitives.
Last updated:  2022-09-08
Cryptographic multilinear maps using pro-p groups
Delaram Kahrobaei and Mima Stanojkovski
Kahrobaei, Tortora, Tota showed how, to any nilpotent group of class n, one can associate a non-interactive key exchange protocol between n+1 users. The multilinear commutator maps associated to nilpotent groups play a key role in this protocol. In the present paper, we explore some alternative platforms, such as pro-p groups.
Last updated:  2022-09-08
Trustless Cross-chain Communication for Zendoo Sidechains
Alberto Garoffolo, Dmytro Kaidalov, and Roman Oliynykov
In the Zendoo white paper we introduced a novel sidechain construction for Bitcoin-like blockchains, which allows a mainchain to create and communicate with sidechains of different types without knowing their internal structure. In this paper, we take a step further by introducing a comprehensive method for sidechains to communicate amongst each other. We will also discuss the details of a cross-chain token transfer protocol that extends the generic communication mechanism. With the cross-chain token transfer protocol, it can enable a broad range of new applications, such as an exchange platform, that allows the ability to trade tokens issued from different sidechains.
Last updated:  2022-09-08
Cryptography with Certified Deletion
James Bartusek and Dakshita Khurana
We propose a new, unifying framework that yields an array of cryptographic primitives with {\em certified deletion}. These primitives enable a party in possession of a quantum ciphertext to generate a classical certificate that the encrypted plaintext has been information-theoretically deleted, and cannot be recovered even given unbounded computational resources. For $X \in \{\mathsf{public}\text{-}\mathsf{key},\mathsf{attribute\text{-}based},\mathsf{fully\text{-}homomorphic},\mathsf{witness},\mathsf{timed}\text{-}\mathsf{release}\}$, our compiler yields post-quantum $X$ encryption with certified deletion, assuming post-quantum $X$ encryption. Assuming the existence of statistically-binding commitments, our compiler yields statistically-binding commitments with certified everlasting hiding as well as statistically-sound zero-knowledge proofs for QMA with certified everlasting zero-knowledge. We also introduce and construct information-theoretic secret sharing with certified deletion. While encryption with certified deletion was first introduced by Broadbent and Islam (TCC 2020) in the context of an information-theoretic one-time pad, existing proposals by Unruh (Eurocrypt 2014), Hiroka et al. (Asiacrypt 2021), Hiroka et al. (Crypto 2021), and Poremba (QIP 2022) for {\em public-key} primitives with certified deletion (1) have complex tailored constructions and non-generic proofs, (2) are not known to satisfy everlasting security after deletion in the plain model, and in many cases (3) resort to idealized models or stronger cryptographic assumptions like obfuscation. We remedy this situation by developing a novel proof technique to argue that a bit $b$ has been {\em information-theoretically deleted} from an adversary's view once they produce a valid deletion certificate, despite having been previously {\em information-theoretically determined} by the ciphertext they held in their view. This may be of independent interest. Finally, we take the notion of certified deletion a step further, and explore its implications in the context of mistrustful two-(and multi-)party cryptography. Here, there is a strong impossibility result by Unruh (Crypto 2013) building on Lo, Chau, and Mayers (Physical Review Letters) showing that everlasting security against \emph{every} party is impossible to achieve, even with quantum communication, and even if parties are computationally bounded during the protocol. Nevertheless, we introduce the notion of \emph{Everlasting Security Transfer}, enabling participants to dynamically request that \emph{any} party (or parties) information-theoretically delete their data, even \emph{after} the protocol execution completes. We show how to construct secure two-party and multi-party computation satisfying this notion of security, which is impossible to achieve in a classical world. Our constructions all assume only statistically-binding commitments, which can be built from one-way functions or pseudo-random quantum states.
Last updated:  2022-09-08
Liberating TFHE: Programmable Bootstrapping with General Quotient Polynomials
Marc Joye and Michael Walter
All known instantiations for fully homomorphic encryption (FHE) produce noisy ciphertexts and rely on a technique called bootstrapping to reduce the noise so as to enable an arbitrary number of homomorphic operations. Bootstrapping is the main performance bottleneck and arguably the biggest obstacle to widespread adoption of FHE. Among the FHE schemes, TFHE and its variations present the appealing property of having a bootstrapping procedure---as well as its extension to programmable bootstrapping---that is relatively light-weight. The essential operations consist of a series of multiplications in $(Z/qZ)[X]/(X^N+1)$. While the NTT is seemingly the natural candidate for evaluating these multiplications in a fast and exact way, it restricts the possible choices for $q$ and $N$. To the authors' knowledge, all current implementations of TFHE with $q$ a power of two actually employ the FFT over the complex numbers instead. This introduces real numbers to the otherwise purely discrete algorithms, including all the drawbacks of the need to approximate them using finite precision. This work studies the avenues available to apply the NTT in the context of TFHE-like schemes. In particular, it considers various combinations of coefficient rings and quotient polynomials that are compatible with the requirements of the underlying scheme. Importantly, this work provides methods for adapting the (programmable) bootstrapping to quotient polynomials beyond power-of-two cyclotomics. As a side effect, it also demonstrates how this may enhance the programmability of the bootstrapping.
Last updated:  2022-09-08
Anonymous Public Key Encryption under Corruptions
Zhengan Huang, Junzuo Lai, Shuai Han, Lin Lyu, and Jian Weng
Anonymity of public key encryption (PKE) requires that, in a multi-user scenario, the PKE ciphertexts do not leak information about which public keys are used to generate them. Corruptions are common threats in the multi-user scenario but anonymity of PKE under corruptions is less studied in the literature. In TCC 2020, Benhamouda et al. first provide a formal characterization for anonymity of PKE under a specific type of corruption. However, no known PKE scheme is proved to meet their characterization. To the best of our knowledge, all the PKE application scenarios which require anonymity also require confidentiality. However, in the work by Benhamouda et al., different types of corruptions for anonymity and confidentiality are considered, which can cause security pitfalls. What's worse, we are not aware of any PKE scheme which can provide both anonymity and confidentiality under the same types of corruptions. In this work, we introduce a new security notion for PKE called ANON-RSO$_k\&$C security, capturing anonymity under corruptions. We also introduce SIM-RSO$_k\&$C security which captures confidentiality under the same types of corruptions. We provide a generic framework of constructing PKE scheme which can achieve the above two security goals simultaneously based on a new primitive called key and message non-committing encryption (KM-NCE). Then we give a general construction of KM-NCE utilizing a variant of hash proof system (HPS) called Key-Openable HPS. We also provide Key-Openable HPS instantiations based on the matrix decisional Diffie-Hellman assumption. Therefore, we can obtain various concrete PKE instantiations achieving the two security goals in the standard model with compact ciphertexts. Furthermore, for some PKE instantiation, its security reduction is tight.
Last updated:  2022-09-08
A Cryptanalysis of NOVA Signature Scheme
Dongyu Wu
NOVA signature scheme is a UOV-type signature scheme over a non-commutative coefficient ring with a novel structural map. In this article we show that a randomly generated central map for the scheme is very likely insecure and may suffer from a forgery attack in polynomial time.
Last updated:  2022-09-08
Ibex: Privacy-preserving ad conversion tracking and bidding (full version)
Ke Zhong, Yiping Ma, and Sebastian Angel
This paper introduces Ibex, an advertising system that reduces the amount of data that is collected on users while still allowing advertisers to bid on real-time ad auctions and measure the effectiveness of their ad campaigns. Specifically, Ibex addresses an issue in recent proposals such as Google’s Privacy Sandbox Topics API in which browsers send information about topics that are of interest to a user to advertisers and demand-side platforms (DSPs). DSPs use this information to (1) determine how much to bid on the auction for a user who is interested in particular topics, and (2) measure how well their ad campaign does for a given audience (i.e., measure conversions). While Topics and related proposals reduce the amount of user information that is exposed, they still reveal user preferences. In Ibex, browsers send user information in an encrypted form that still allows DSPs and advertisers to measure conversions, compute aggregate statistics such as histograms about users and their interests, and obliviously bid on auctions without learning for whom they are bidding. Our implementation of Ibex shows that creating histograms is 1.7–2.5× more expensive for browsers than disclosing user information, and Ibex’s oblivious bidding protocol can finish auctions within 550 ms. We think this makes Ibex capable of preserving a good experience while improving user privacy.
Last updated:  2022-09-20
Secure Maximum Weight Matching Approximation on General Graphs (Full Version)
Andreas Brüggemann, Malte Breuer, Andreas Klinger, Thomas Schneider, and Ulrike Meyer
Privacy-preserving protocols for matchings on general graphs can be used for applications such as online dating, bartering, or kidney donor exchange. In addition, they can act as a building blocks for more complex protocols. While privacy preserving protocols for matchings on bipartite graphs are a well-researched topic, the case of general graphs has experienced significantly less attention so far. We address this gap by providing the first privacy-preserving protocol for maximum weight matching on general graphs. We present two protocol variants, which both compute an $1/2-$approximation instead of an optimal solution in favor of scalability. For $N$ nodes, the first variant requires $\mathcal{O}(N \log^2 N)$ rounds and $\mathcal{O}(N^3\log N)$ communication, and the second variant requires only $\mathcal{O}(N \log N)$ rounds and $\mathcal{O}(N^3)$ communication. We implement both variants and find that the first variant runs in $14.9$ minutes for $N=300$ nodes, while the second variant requires only $5.1$ minutes for $N=300$, and $12.5$ minutes for $N=400$.
Last updated:  2022-09-07
On the security of keyed hashing based on an unkeyed block function
Jonathan Fuchs, Yann Rotella, and Joan Daemen
In this paper we study the security of two constructions for variable-length universal hash functions by means of their universality. Both constructions make use of a fixed-length unkeyed function that we call a block function. One construction is serial and is an idealization of the compression phase of Pelican-MAC. The other construction is parallel and is an idealization of the compression phase of Farfalle. Both are instances of a class of functions we call semi-group accumulators. We prove that the universality of these constructions is fully determined by the differential probability of block function differentials and, if not a permutation, the relative frequency of block function outputs. We show that both block function parallelization and serialization have equal security (against forgery) in the Wegman-Carter(-Shoup) construction. However, for the block functions we target, parallelization can provide significantly better security than serialization in the Protected Hash (PH) construction. Moreover, below a certain data limit, PH provides better security than WC(S) for the block function parallelization, despite the fact that it does not require a nonce. We show evidence of this effect by taking Xoodoo[3] as the block function .
Last updated:  2022-09-07
No More Attacks on Proof-of-Stake Ethereum?
Francesco D'Amato, Joachim Neu, Ertem Nusret Tas, and David Tse
The latest message driven (LMD) greedy heaviest observed sub-tree (GHOST) consensus protocol is a critical component of future proof-of-stake (PoS) Ethereum. In its current form, the protocol is brittle and intricate to reason about, as evidenced by recent attacks, patching attempts, and Görli testnet reorgs. We present Goldfish, which can be seen as a considerably simplified variant of the current protocol, and prove that it is secure and reorg resilient in synchronous networks with dynamic participation, assuming a majority of the nodes (called validators) follows the protocol honestly. Furthermore, we show that subsampling validators can improve the communication efficiency of Goldfish, and that Goldfish is composable with finality gadgets and accountability gadgets. The aforementioned properties make Goldfish a credible candidate for a future protocol upgrade of PoS Ethereum, as well as a versatile pedagogical example. Akin to traditional propose-and-vote-style consensus protocols, Goldfish is organized into slots, at the beginning of which a leader proposes a block containing new transactions, and subsequently members of a committee take a vote towards block confirmation. But instead of using quorums, Goldfish is powered by a new mechanism that carefully synchronizes the inclusion and exclusion of votes in honest validators' views.
Last updated:  2022-09-23
TRIFORS: LINKable Trilinear Forms Ring Signature
Giuseppe D'Alconzo and Andrea Gangemi
We present TRIFORS (TRIlinear FOrms Ring Signature), a logarithmic post-quantum (linkable) ring signature based on a novel assumption regarding equivalence of alternating trilinear forms. The basis of this work is the construction by Beullens, Katsumata and Pintore from Asiacrypt 2020 to obtain a linkable ring signature from a cryptographic group action. The group action on trilinear forms used here is the same employed in the signature presented by Tang et al. at Eurocrypt 2022. We first define a sigma protocol that, given a set of public keys, the ring, allows to prove the knowledge of a secret key corresponding to a public one in the ring. Furthermore, some optimisations are used to reduce the size of the signature: among others, we use a novel application of the combinatorial number system to the space of the challenges. Using the Fiat-Shamir transform, we obtain a (linkable) ring signature of competitive length with the state-of-the-art among post-quantum proposals for security levels 128 and 192.
Last updated:  2022-09-07
DyCAPS: Asynchronous Proactive Secret Sharing for Dynamic Committees
Bin Hu, Zongyang Zhang, Han Chen, You Zhou, Huazu Jiang, and Jianwei Liu
Dynamic-committee proactive secret sharing (DPSS) enables the update of secret shares and the alternation of shareholders, which makes it a promising technology for long-term key management and committee governance. However, there is a huge gap in communication costs between the state-of-the-art asynchronous and non-asynchronous DPSS schemes. In this paper, we fill this gap and propose the first practical DPSS scheme, DyCAPS, with a cubic communication cost w.r.t. the number of shareholders. DyCAPS can be efficiently integrated into existing asynchronous BFT-based blockchains to support the member change in BFT committees, without increasing the overall asymptotic communication cost. The experimental results show that DyCAPS introduces acceptable latency during the reconfiguration of the committees.
Last updated:  2022-09-07
Multi-Input Quadratic Functional Encryption: Stronger Security, Broader Functionality
Shweta Agrawal, Rishab Goyal, and Junichi Tomida
Multi-input functional encryption, MIFE, is a powerful generalization of functional encryption that allows computation on encrypted data coming from multiple different data sources. In a recent work, Agrawal, Goyal, and Tomida (CRYPTO 2021) constructed MIFE for the class of quadratic functions. This was the first MIFE construction from bilinear maps that went beyond inner product computation. We advance the state-of-the-art in MIFE, and propose new constructions with stronger security and broader functionality. Stronger Security: In the typical formulation of MIFE security, an attacker is allowed to either corrupt all or none of the users who can encrypt the data. In this work, we study MIFE security in a stronger and more natural model where we allow an attacker to corrupt any subset of the users, instead of only permitting all-or-nothing corruption. We formalize the model by providing each user a unique encryption key, and letting the attacker corrupt all non-trivial subsets of the encryption keys, while still maintaining the MIFE security for ciphertexts generated using honest keys. We construct a secure MIFE system for quadratic functions in this fine-grained corruption model from bilinear maps. Our construction departs significantly from the existing MIFE schemes as we need to tackle a more general class of attackers. Broader Functionality: The notion of multi-client functional encryption, MCFE, is a useful extension of MIFE. In MCFE, each encryptor can additionally tag each ciphertext with appropriate metadata such that ciphertexts with only matching metadata can be decrypted together. In more detail, each ciphertext is now annotated with a unique label such that ciphertexts encrypted for different slots can now only be combined together during decryption as long as the associated labels are an exact match for all individual ciphertexts. In this work, we upgrade our MIFE scheme to also support ciphertext labelling. While the functionality of our scheme matches that of MCFE for quadratic functions, our security guarantee falls short of the general corruption model studied for MCFE. In our model, all encryptors share a secret key, therefore this yields a secret-key version of quadratic MCFE, which we denote by SK-MCFE. We leave the problem of proving security in the general corruption model as an important open problem.
Last updated:  2022-09-07
META-BTS: Bootstrapping Precision Beyond the Limit
Youngjin Bae, Jung Hee Cheon, Wonhee Cho, Jaehyung Kim, and Taekyung Kim
Bootstrapping, which enables the full homomorphic encryption scheme that can perform an infinite number of operations by restoring the modulus of the ciphertext with a small modulus, is an essential step in homomorphic encryption. However, bootstrapping is the most time and memory consuming of all homomorphic operations. As we increase the precision of bootstrapping, a large amount of computational resources is required. Specifically, for any of the previous bootstrap designs, the precision of bootstrapping is limited by rescaling precision. In this paper, we propose a new bootstrapping algorithm of the Cheon-Kim-Kim-Song (CKKS) scheme to use a known bootstrapping algorithm repeatedly, so called { Meta-BTS}. By repeating the original bootstrapping operation twice, one can obtain another bootstrapping with its precision essentially doubled; it can be generalized to be $k$-fold bootstrapping operations for some $k>1$ while the ciphertext size is large enough. Our algorithm overcomes the precision limitation given by the rescale operation.
Last updated:  2022-09-07
McEliece-type encryption based on Gabidulin codes with no hidden structure
Wenshuo Guo and Fang-Wei Fu
This paper presents a new McEliece-type encryption scheme based on Gabidulin codes, which uses linearized transformations to disguise the private key. When endowing this scheme with the partial cyclic structure, we obtain a public key of the form $GM^{-1}$, where $G$ is a partial circulant generator matrix of Gabidulin code and $M$ as well as $M^{-1}$ is a circulant matrix of large rank weight, even as large as the code length. Another difference from Loidreau's proposal at PQCrypto 2017 is that both $G$ and $M$ are publicly known. Recovering the private key can be reduced to deriving from $M$ a linearized transformation and two circulant matrices of small rank weight. This new scheme is shown to resist all the known distinguisher-based attacks, such as the Overbeck attack and Coggia-Couvreur attack, and also has a very small public key size. For instance, 2592 bytes are enough for our proposal to achieve the security of 256 bits, which is 400 times smaller than Classic McEliece that has been selected into the fourth round of the NIST Post-Quantum Cryptography (PQC) standardization process.
Last updated:  2022-09-06
A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem
Christopher Battarbee, Delaram Kahrobaei, Ludovic Perret, and Siamak F. Shahandashti
Group-based cryptography is a relatively young family in post-quantum cryptography. In this paper we give the first dedicated security analysis of a central problem in group-based cryptography: the so-called Semidirect Product Key Exchange(SDPKE). We present a subexponential quantum algorithm for solving SDPKE. To do this we reduce SDPKE to the Abelian Hidden Shift Problem (for which there are known quantum subexponential algorithms). We stress that this does not per se constitute a break of SDPKE; rather, the purpose of the paper is to provide a connection to known problems.
Last updated:  2022-09-06
Point-Halving and Subgroup Membership in Twisted Edwards Curves
Thomas Pornin
In this short note, we describe a process for halving a point on a twisted Edwards curve. This can be used to test whether a given point is in the subgroup of prime order $\ell$, which is used by some cryptographic protocols. On Curve25519, this new test is about twice faster than the classic method consisting of multiplying the source point by $\ell$.
Last updated:  2022-09-06
A Third is All You Need: Extended Partial Key Exposure Attack on CRT-RSA with Additive Exponent Blinding
Yuanyuan Zhou, Joop van de Pol, Yu Yu, and François-Xavier Standaert
At Eurocrypt 2022, May et al. proposed a partial key exposure (PKE) attack on CRT-RSA that efficiently factors $N$ knowing only a $\frac{1}{3}$-fraction of either most significant bits (MSBs) or least significant bits (LSBs) of private exponents $d_p$ and $d_q$ for public exponent $e \approx N^{\frac{1}{12}}$. In practice, PKE attacks typically rely on the side-channel leakage of these exponents, while a side-channel resistant implementation of CRT-RSA often uses additively blinded exponents $d^{\prime}_p = d_p + r_p(p-1)$ and $d^{\prime}_q = d_q + r_q(q-1)$ with unknown random blinding factors $r_p$ and $r_q$, which makes PKE attacks more challenging. Motivated by the above, we extend the PKE attack of May et al. to CRT-RSA with additive exponent blinding. While admitting $r_pe\in(0,N^{\frac{1}{4}})$, our extended PKE works ideally when $r_pe \approx N^{\frac{1}{12}}$, in which case the entire private key can be recovered using only $\frac{1}{3}$ known MSBs or LSBs of the blinded CRT exponents $d^{\prime}_p$ and $d^{\prime}_q$. Our extended PKE follows their novel two-step approach to first compute the key-dependent constant $k^{\prime}$ ($ed^{\prime}_p = 1 + k^{\prime}(p-1)$, $ed^{\prime}_q = 1 + l^{\prime}(q-1)$), and then to factor $N$ by computing the root of a univariate polynomial modulo $k^{\prime}p$. We extend their approach as follows. For the MSB case, we propose two options for the first step of the attack, either by obtaining a single estimate $k^{\prime}l^{\prime}$ and calculating $k^{\prime}$ via factoring, or by obtaining multiple estimates $k^{\prime}l^{\prime}_1,\ldots,k^{\prime}l^{\prime}_z$ and calculating $k^{\prime}$ probabilistically via GCD. For the LSB case, we extend their approach by constructing a different univariate polynomial in the second step of the LSB attack. A formal analysis shows that our LSB attack runs in polynomial time under the standard Coppersmith-type assumption, while our MSB attack either runs in sub-exponential time with a reduced input size (the problem is reduced to factor a number of size $e^2r_pr_q\approx N^{\frac{1}{6}}$) or in probabilistic polynomial time under a novel heuristic assumption. Under the settings of the most common key sizes (1024-bit, 2048-bit, and 3072-bit) and blinding factor lengths (32-bit, 64-bit, and 128-bit), our experiments verify the validity of the Coppersmith-type assumption and our own assumption, as well as the feasibility of the factoring step. To the best of our knowledge, this is the first PKE on CRT-RSA with experimentally verified effectiveness against 128-bit unknown exponent blinding factors. We also demonstrate an application of the proposed PKE attack using real partial side-channel key leakage targeting a Montgomery Ladder exponentiation CRT implementation.
Last updated:  2022-09-06
Pairings in Rank-1 Constraint Systems
Youssef El Housni
Bilinear pairings have been used in different cryptographic applications and demonstrated to be a key building block for a plethora of constructions. In particular, some Succinct Non-interactive ARguments of Knowledge (SNARKs) have very short proofs and very fast verifi- cation thanks to a multi-pairing computation. This succinctness makes pairing-based SNARKs suitable for proof recursion, that is proofs veri- fying other proofs. In this scenario one requires to express efficiently a multi-pairing computation as a SNARK arithmetic circuit. Other com- pelling applications such as verifying Boneh–Lynn–Shacham (BLS) sig- natures or Kate–Zaverucha–Goldberg (KZG) polynomial commitment opening in a SNARK fall into the same requirement. The implementation of pairings is challenging but the literature has very detailed approaches on how to reach practical and optimized implementations in different contexts and for different target environments. However, to the best of our knowledge, no previous publication has addressed the question of ef- ficiently implementing a pairing as a SNARK arithmetic circuit. In this work, we consider efficiently implementing pairings in Rank-1 Constraint Systems (R1CS), a widely used model to express SNARK statements. We implement our techniques in the gnark open-source ecosystem and show that the arithmetic circuit depth can be almost halved compared to the previously best known pairing implementation on a Barreto–Lynn–Scott (BLS) curve of embedding degree 12, resulting in a significantly faster proving time. We also investigate and implement the case of BLS curves of embedding degree 24.
Last updated:  2022-09-06
Group-based Cryptography in the Quantum Era
Delaram Kahrobaei, Ramón Flores, and Marialaura Noce
In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic groups and graph groups, dealing in particular with their algorithmic properties and cryptographic applications. We then, describe some applications of combinatorial algebra in fully homomorphic encryption. In the end we discussing several open problems in this direction.
Last updated:  2022-09-06
The Scholz conjecture on addition chain is true for $v(n)= 4$
Amadou TALL
The aim of this paper is to prove that the Scholz conjecture on addition chain is true for all integers with $v(n)=4$, $v(n)$ is the number of ''1'' in the binary expansion of $n$.
Last updated:  2022-09-06
Decomposing Linear Layers
Christof Beierle, Patrick Felke, Gregor Leander, and Sondre Rønjom
There are many recent results on reverse-engineering (potentially hidden) structure in cryptographic S-boxes. The problem of recovering structure in the other main building block of symmetric cryptographic primitives, namely, the linear layer, has not been paid that much attention so far. To fill this gap, in this work, we develop a systematic approach to decomposing structure in the linear layer of a substitution-permutation network (SPN), covering the case in which the specification of the linear layer is obfuscated from applying secret linear transformations to the S-boxes. We first present algorithms to decide whether an $ms \times ms$ matrix with entries in a prime field $\mathbb{F}_p$ can be represented as an $m \times m$ matrix over the extension field $\mathbb{F}_{p^s}$. We then study the case of recovering structure in MDS matrices by investigating whether a given MDS matrix follows a Cauchy construction. As an application, for the first time, we show that the $8 \times 8$ MDS matrix over $\mathbb{F}_{2^8}$ used in the hash function Streebog is a Cauchy matrix.
Last updated:  2022-09-06
Differential Cryptanalysis of K-Cipher
Mohammad Mahzoun, Liliya Kraleva, Raluca Posteuca, and Tomer Ashur
K-Cipher is an ultra-low latency block cipher with variable-length parameters designed by Intel Labs. In this work, we analyze the security of K-Cipher and propose a differential cryptanalysis attack with the complexity of $2^{29.7}$ for a variant of K-Cipher with state size $n=24$ bits state and block size $m=8$ bits. Our attack recovers the secret key and secret randomizer values with a total length of 240 bits in $\sim 30$ minutes on a standard desktop machine. We show that it is possible to extend the same attack for an arbitrary set of parameters.
Last updated:  2022-09-06
Classically Verifiable NIZK for QMA with Preprocessing
Tomoyuki Morimae and Takashi Yamakawa
We propose three constructions of classically verifiable non-interactive zero-knowledge proofs and arguments (CV-NIZK) for QMA in various preprocessing models. 1. We construct a CV-NIZK for QMA in the quantum secret parameter model where a trusted setup sends a quantum proving key to the prover and a classical verification key to the verifier. It is information theoretically sound and zero-knowledge. 2. Assuming the quantum hardness of the learning with errors problem, we construct a CV-NIZK for QMA in a model where a trusted party generates a CRS and the verifier sends an instance-independent quantum message to the prover as preprocessing. This model is the same as one considered in the recent work by Coladangelo, Vidick, and Zhang (CRYPTO '20). Our construction has the so-called dual-mode property, which means that there are two computationally indistinguishable modes of generating CRS, and we have information theoretical soundness in one mode and information theoretical zero-knowledge property in the other. This answers an open problem left by Coladangelo et al, which is to achieve either of soundness or zero-knowledge information theoretically. To the best of our knowledge, ours is the first dual-mode NIZK for QMA in any kind of model. 3. We construct a CV-NIZK for QMA with quantum preprocessing in the quantum random oracle model. This quantum preprocessing is the one where the verifier sends a random Pauli-basis states to the prover. Our construction uses the Fiat-Shamir transformation. The quantum preprocessing can be replaced with the setup that distributes Bell pairs among the prover and the verifier, and therefore we solve the open problem by Broadbent and Grilo (FOCS '20) about the possibility of NIZK for QMA in the shared Bell pair model via the Fiat-Shamir transformation.
Last updated:  2022-09-05
On the security of data markets: controlled Private Function Evaluation
István Vajda
The income of companies working on data markets steadily grows year by year. Private function evaluation (PFE) is a valuable tool in solving corresponding security problems. The task of Controlled Private Function Evaluation (CPFE) and its relaxed version (rCPFE) was proposed in [11]. We define an ideal functionality for the latter task and present a UC-secure realization of the functionality against static malicious parties. The core primitive is functional encryption (FE) and essentially this determines the conditions of realizability. Accordingly, in the case of non-adaptive FE-setting secure realization of the ideal functionality is achievable in the standard model, otherwise, accessibility of random oracle is required.
Last updated:  2022-09-05
Hawk: Module LIP makes Lattice Signatures Fast, Compact and Simple
Léo Ducas, Eamonn W. Postlethwaite, Ludo N. Pulles, and Wessel van Woerden
We propose the signature scheme Hawk, a concrete instantiation of proposals to use the Lattice Isomorphism Problem (LIP) as a foundation for cryptography that focuses on simplicity. This simplicity stems from LIP, which allows the use of lattices such as $\mathbb{Z}^n$ , leading to signature algorithms with no floats, no rejection sampling, and compact precomputed distributions. Such design features are desirable for constrained devices, and when computing signatures inside FHE or MPC. The most significant change from recent LIP proposals is the use of module lattices, reusing algorithms and ideas from NTRUSign and Falcon. Its simplicity makes Hawk competitive. We provide cryptanalysis with experimental evidence for the design of Hawk and implement two parameter sets, Hawk-512 and Hawk-1024. Signing using Hawk-512 and Hawk-1024 is four times faster than Falcon on x86 architectures, produces signatures that are about 15% more compact, and is slightly more secure against forgeries by lattice reduction attacks. When floating-points are unavailable, Hawk signs 15 times faster than Falcon. We provide a worst case to average case reduction for module LIP. For certain parametrisations of Hawk this applies to secret key recovery and we reduce signature forgery in the random oracle model to a new problem called the one more short vector problem.
Last updated:  2022-09-07
Efficient Constant-Time Implementation of SM4 with Intel GFNI instruction set extension and Arm NEON coprocessor
Weiji Guo
The efficiency of constant-time SM4 implementation has been lagging behind that of AES for most internet traffic and applicable data encryption scenarios. The best performance before our works was 3.77 cpb for x86 platform (AESNI + AVX2), and 8.62 cpb for Arm platform (NEON). Meanwhile the state of art constant-time AES implementation could reach 0.63 cpb. Dedicated SM4 instruction set extensions like those optionally available in Armv8.2, could achieve comparable cpb to AES. But they are only available in limited processors, therefore does not impact much to real-world uses. To fill the gap we explored some novel techniques with Intel GFNI instruction set extension and Arm NEON coprocessor. We achieved 1.51 cpb with GFNI + AVX512 and 2.62 cpb with GFNI + AVX2 for Intel processors; we also achieved 6.74 cpb with NEON. In addition, we simplified the algebraic expression of SM4 S-Box. And our technique to exploit L1 cache could also be applied to other applications and hardware platforms if the circumstances apply.
Last updated:  2022-09-06
Sharp: Short Relaxed Range Proofs
Geoffroy Couteau, Dahmun Goudarzi, Michael Klooß, and Michael Reichle
We provide optimized range proofs, called $\mathsf{Sharp}$, in discrete logarithm and hidden order groups, based on square decomposition. In the former setting, we build on the paradigm of Couteau et al. (Eurocrypt '21) and optimize their range proof (from now on, CKLR) in several ways: (1) We introduce batching via vector commitments and an adapted $\Sigma$-protocol. (2) We introduce a new group switching strategy to reduce communication. (3) As repetitions are necessary to instantiate CKLR in standard groups, we provide a novel batch shortness test that allows for cheaper repetitions. The analysis of our test is nontrivial and forms a core technical contribution of our work. For example, for $\kappa = 128$ bit security and $B = 64$ bit ranges for $N = 1$ (resp. $N = 8$) proof(s), we reduce the proof size by $34\%$ (resp. $75\%$) in arbitrary groups, and by $66\%$ (resp. $88\%)$ in groups of order $256$-bit, compared to CKLR. As $\mathsf{Sharp}$ and CKLR proofs satisfy a “relaxed” notion of security, we show how to enhance their security with one additional hidden order group element. In RSA groups, this reduces the size of state of the art range proofs (Couteau et al., Eurocrypt '17) by $77\%$ ($\kappa = 128, B = 64, N = 1$). Finally, we implement our most optimized range proof. Compared to the state of the art Bulletproofs (Bünz et al., S&P 2018), our benchmarks show a very significant runtime improvement. Eventually, we sketch some applications of our new range proofs.
Last updated:  2022-09-14
Fully Collusion Resistant Trace-and-Revoke Functional Encryption for Arbitrary Identities
Fucai Luo, Saif Al-Kuwari, Haiyan Wang, and Xingfu Yan
Functional Encryption (FE) has been extensively studied in the recent years, mainly focusing on the feasibility of constructing FE for general functionalities, as well as some realizations for restricted functionalities of practical interest, such as inner-product. However, little consideration has been given to the issue of key leakage on FE. The property of FE that allows multiple users to obtain the same functional keys from the holder of the master secret key raises an important problem: if some users leak their keys or collude to create a pirated decoder, how can we identify at least one of those users, given some information about the compromised keys or the pirated decoder? Moreover, how do we disable the decryption capabilities of those users (i.e. traitors)? Two recent works have offered potential solutions to the above traitor scenario. However, the two solutions satisfy weaker notions of security and traceability, can only tolerate bounded collusions (i.e., there is an a priori bound on the number of keys the pirated decoder obtains), or can only handle a polynomially large universe of possible identities. In this paper, we study trace-and-revoke mechanism on FE and provide the first construction of trace-and-revoke FE that supports arbitrary identities, is both fully collusion resistant and fully anonymous. Our construction relies on a generic transformation from revocable predicate functional encryption with broadcast (RPFE with broadcast, which is an extension of revocable predicate encryption with broadcast proposed by Kim and J. Wu at ASIACRYPT'2020) to trace-and-revoke FE. Since this construction admits a generic construction of trace-and-revoke inner-product FE (IPFE), we instantiate the trace-and-revoke IPFE from the well-studied Learning with Errors (LWE). This is achieved by proposing a new LWE-based attribute-based IPFE (ABIPFE) scheme to instantiate RPFE with broadcast.
Last updated:  2022-09-05
A Survey on Exotic Signatures for Post-Quantum Blockchain: Challenges & Research Directions
Maxime Buser, Rafael Dowsley, Muhammed F. Esgin, Clémentine Gritti, Shabnam Kasra Kermanshahi, Veronika Kuchta, Jason T. LeGrow, Joseph K. Liu, Raphael C.-W. Phan, Amin Sakzad, Ron Steinfeld, and Jiangshan Yu
Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this paper, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and which are crucial cryptographic tools used in the blockchain ecosystem for (i) account management, (ii) consensus efficiency, (iii) empowering scriptless blockchain, and (iv) privacy. The exotic signatures that we particularly focus on in this work are the following: multi-/aggregate, threshold, adaptor, blind and ring signatures. Herein the term exotic refers to signatures with properties which are not just beyond the norm for signatures e.g. unforgeability, but also imbue new forms of functionalities. Our treatment of such exotic signatures includes discussions on existing challenges and future research directions in the post-quantum space. We hope that this article will help to foster further research to make post-quantum cryptography more accessible so that blockchain systems can be made ready in advance of the approaching quantum threats.
Last updated:  2022-09-05
Farasha: A Provable Permutation-based Parallelizable PRF
Najwa Aaraj, Emanuele Bellin, Ravindra Jejurikar, Marc Manzano, Raghvendra Rohit, and Eugenio Salazar
The pseudorandom function Farfalle, proposed by Bertoni et al. at ToSC 2017, is a permutation based arbitrary length input and output PRF. At its core are the public permutations and feedback shift register based rolling functions. Being an elegant and parallelizable design, it is surprising that the security of Farfalle has been only investigated against generic cryptanalysis techniques such as differential/linear and algebraic attacks and nothing concrete about its provable security is known. To fill this gap, in this work, we propose Farasha, a new permutation-based parallelizable PRF with provable security. Farasha can be seen as a simple and provable Farfalle-like construction where the rolling functions in the compression and expansion phases of Farfalle are replaced by a uniform almost xor universal (AXU) and a simple counter, respectively. We then prove that in the random permutation model, the compression phase of Farasha can be shown to be an uniform AXU function and the expansion phase can be mapped to an Even-Mansour block cipher. Consequently, combining these two properties, we show that Farasha achieves a security of min(keysize, permutation size/2). Finally, we provide concrete instantiations of Farasha with AXU functions providing different performance trade-offs. We believe our work will bring new insights in further understanding the provable security of Farfalle-like constructions.
Last updated:  2022-09-21
Secure Anycast Channels with Applications to 4G and 5G Handovers
Karl Norrman
In 3GPP mobile networks, application data is transferred between the phone and an access point over a wireless link. The mobile network wireless link is special since one channel endpoint is handed over from one access point to another as the phone physically moves. Key evolution during handover has been analyzed in various works, but these do not combine the analysis with analysis of the wireless-link application-data encryption protocol that uses the keys. To enable formal analysis of the 4G/5G wireless link, we develop a game-based security framework for such channels and define flexible key insulation security notions for application data transfer, including forward and backward security in the given adversary model. Our notions are modular and combine a bidirectional application data transfer channel with a generic framework for multiparty channel-evolution protocols. These two components interact, and the security of the channel-evolution protocol may rely on the security of the data transfer channel for some or all its messages. We also develop the first formal model of 4G/5G wireless link security including both handover key evolution and application data transfer, in the complexity theoretic setting. We prove the model secure w.r.t. our security notions. As a byproduct, we identify recommendations for improving the security of future mobile network standards to achieve key insulation. Specifically, we show that the current standards do not achieve forward secure encryption, even though this appears to be an explicit goal. We show how this can be rectified.
Last updated:  2022-09-04
On Security Against Time Traveling Adversaries
Lúcás Críostóir Meier
If you had a time machine, what cryptography would you be able to break? In this work, we investigate the notion of time travel, formally defining models for adversaries equipped with a time machine, and exploring the consequences for cryptography. We find that being able to rewind time breaks some cryptographic schemes, and being able to freely move both forwards and backwards in time breaks even more schemes. We look at the impacts of time travel on encryption and signatures in particular, finding that the $\text{IND-CCA}$ and $\text{EUF-CMA}$ security games are broken, while $\text{IND-CPA}$ and $\text{UUF-CMA}$ remain secure.
Last updated:  2022-09-04
Finding the Impossible: Automated Search for Full Impossible Differential, Zero-Correlation, and Integral Attacks (Preliminary Version)
Hosein Hadipour, Sadegh Sadeghi, and Maria Eichlseder
Impossible differential (ID) and zero-correlation (ZC) attacks are a family of important attacks on block ciphers. For example, the impossible differential attack was the first cryptanalytic attack on 7 rounds of AES. Evaluating the security of block ciphers against these attacks is very important, but also challenging: Finding these attacks usually implies a combinatorial optimization problem involving many parameters and constraints that is very hard to solve using manual approaches. Automated solvers, such as Constraint Programming (CP) solvers, can help the cryptanalyst to find suitable distinguishers. However, previous CP-based methods are focused on finding only the ID or ZC distinguishers, and often only in a limited search space. Notably, none of them can be extended to a unified optimization problem for finding full attacks including efficient key-recovery steps. In this paper, we present a new CP-based method to search for ID and ZC distinguishers and extend it to a unified constraint optimization problem for finding full ID, ZC, and integral attacks. To show the effectiveness and usefulness of our method, we apply it to the ISO standard block cipher SKINNY and improve all of the existing ID, ZC, and integral attacks on it. In particular, we improve the integral attacks on SKINNY-$n$-$3n$ and SKINNY-$n$-$2n$ by 3 and 2 rounds, respectively, obtaining the best cryptanalytic results on these variants in the single-key setting. We improve the ZC attack on SKINNY-$n$-$2n$ and SKINNY-$n$-$n$ by 1 and 2 rounds, respectively. Applying our tool to discover ID attacks, we improve the ID attacks on all variants of SKINNY in the single-tweakey setting. Particularly, we improve the time complexity of the best previous single key ID attack on SKINNY-$128$-$256$ by a factor of $2^{22.57}$, while keeping the data and memory complexities much smaller. We also improve the ID attack on SKINNY-$n$-$3n$ in the related-tweakey setting. Our method is generic and applicable to other word-oriented block ciphers.
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